{"id":13359,"date":"2025-05-01T07:31:19","date_gmt":"2025-05-01T07:31:19","guid":{"rendered":"https:\/\/www.hnjournal.net\/?page_id=13359"},"modified":"2025-05-01T07:31:21","modified_gmt":"2025-05-01T07:31:21","slug":"6-5-31","status":"publish","type":"page","link":"https:\/\/www.hnjournal.net\/en\/6-5-31\/","title":{"rendered":""},"content":{"rendered":"<div class=\"journal-article\" style=\"margin-bottom: 20px;\"><h3 style='text-align: right; font-family:Simplified Arabic;'>\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0646\u0645\u0627\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062c\u0632\u0627\u0626\u064a\u0629 \u0644\u062d\u0644 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a \u0648\u062a\u0639\u062f\u062f \u0627\u0644\u0627\u0628\u0639\u0627\u062f<\/h3><p style='text-align:right; font-weight:bold; direction:rtl;'>\u0631\u062c\u0627\u0621 \u0623\u0645\u062d\u0645\u062f \u0639\u0644\u0649 \u0644\u0634\u0647\u0628 <sup>1<\/sup>\u060c \u0641\u0631\u062c \u0635\u0627\u0644\u062d \u0633\u0627\u0637\u064a<sup>2<\/sup>\u060c \u0639\u0628\u062f\u0627\u0644\u0628\u0627\u0633\u0637 \u0639\u0628\u062f\u0627\u0644\u0644\u0647 \u0627\u0644\u0639\u0645\u0631\u0648\u0646\u064a<sup>3<\/sup>\u060c \u0641\u0627\u064a\u0632\u0629 \u0641\u0631\u062c \u0627\u0644\u062e\u0641\u064a\u0641\u064a<sup>3<\/sup> \u060c \u0623\u062d\u0645\u062f \u0645\u062d\u0645\u062f \u0645\u0627\u0645\u064a<sup>3<\/sup><\/p><div style='direction:rtl; text-align:right; font-size:12px; line-height:1.5;'><p><sup>1<\/sup>- \u0642\u0633\u0645 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a\u060c \u0643\u0644\u064a\u0629 \u0627\u0644\u0639\u0644\u0648\u0645\u060c \u062c\u0627\u0645\u0639\u0629 \u0627\u0644\u062c\u0641\u0631\u0629\u060c \u0627\u0644\u062c\u0641\u0631\u0629\u060c \u0644\u064a\u0628\u064a\u0627<\/p><p><sup>2<\/sup>- \u0642\u0633\u0645 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a\u060c \u0643\u0644\u064a\u0629 \u0627\u0644\u0622\u062f\u0627\u0628 \u0648\u0627\u0644\u0639\u0644\u0648\u0645 \u0627\u0644\u0648\u0627\u062d\u0627\u062a\u060c \u062c\u0627\u0644\u0648\u060c \u062c\u0627\u0645\u0639\u0629 \u0628\u0646\u063a\u0627\u0632\u064a\u060c \u0644\u064a\u0628\u064a\u0627<\/p><p><sup>3<\/sup>- \u0642\u0633\u0645 \u0627\u0644\u0625\u062d\u0635\u0627\u0621\u060c \u0643\u0644\u064a\u0629 \u0627\u0644\u0639\u0644\u0648\u0645\u060c \u062c\u0627\u0645\u0639\u0629 \u0628\u0646\u063a\u0627\u0632\u064a\u060c \u0628\u0646\u063a\u0627\u0632\u064a\u060c \u0644\u064a\u0628\u064a\u0627<\/p><\/div><h4 style='text-align:left; direction:ltr; unicode-bidi:embed; font-family:Times New Roman;'>In using Penalized Regression Models to solve the Multicollinearity and Multidimensional Problem<\/h4><p style='text-align:left; font-weight:bold; direction:ltr; margin-top:12px;'>Raja Amhamed Ali Lashhab<sup>1<\/sup>, Faraj Saleh Sati<sup>2<\/sup>, Abdulbasit Abdullah Al-Amruni<sup>3<\/sup>, Faiza Faraj Al-Khafifi<sup>3<\/sup>, Ahmed Mohammed Mami<sup>3<\/sup><\/p><div style='direction:ltr; text-align:left; font-size:12px; line-height:1.7; margin-bottom:10px;'><p style='margin:0 0 8px 0;'><sup>1<\/sup> Department of Mathematics, Faculty of Science, Al-Jufra University, Libya.<\/p><p style='margin:0 0 8px 0;'><sup>2<\/sup> Department of Mathematics, Faculty of Arts and Sciences Al-Wahat, Jalu, University of Benghazi, Libya.<\/p><p style='margin:0 0 8px 0;'><sup>3<\/sup> Department of Statistics, Faculty of Science, University of Benghazi, Libya.<\/p><\/div><p style='text-align:left;'><strong>DOI:<\/strong> <a href='https:\/\/doi.org\/https:\/\/doi.org\/10.53796\/hnsj65\/31' target='_blank' rel='noopener'>https:\/\/doi.org\/10.53796\/hnsj65\/31<\/a><\/p><p style='text-align: right;'><strong>\u0627\u0644\u0645\u0639\u0631\u0641 \u0627\u0644\u0639\u0644\u0645\u064a \u0627\u0644\u0639\u0631\u0628\u064a \u0644\u0644\u0623\u0628\u062d\u0627\u062b:<\/strong> <a href='https:\/\/arsri.org\/10000\/65\/31' target='_blank' rel='noopener'>https:\/\/arsri.org\/10000\/65\/31<\/a><\/p><p style='text-align: right;'><strong>\u0627\u0644\u0645\u062c\u0644\u062f (6) \u0627\u0644\u0639\u062f\u062f (5). \u0627\u0644\u0635\u0641\u062d\u0627\u062a:<\/strong> 474 - 490<\/p><p style='text-align: right;'><strong>\u062a\u0627\u0631\u064a\u062e \u0627\u0644\u0627\u0633\u062a\u0642\u0628\u0627\u0644:<\/strong> 2025-04-07 | <strong>\u062a\u0627\u0631\u064a\u062e \u0627\u0644\u0642\u0628\u0648\u0644:<\/strong> 2025-04-15 | <strong>\u062a\u0627\u0631\u064a\u062e \u0627\u0644\u0646\u0634\u0631:<\/strong> 2025-05-01<\/p><p><a href='\/volume6\/issue5\/6-5-31.pdf' target='_blank' rel='noopener' style='background-color:green;color:white;padding:10px 15px;text-decoration:none;border-radius:5px;'>Download PDF<\/a><\/p>\r\n<style>\r\n.hnsj-cite-btn{\r\n  display:inline-flex; 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A. A, Sati F. S, Al-Amruni A. A, Al-Khafifi F. F, Mami A. M. (2025). In using Penalized Regression Models to solve the Multicollinearity and Multidimensional Problem. Humanities &amp; Natural Sciences Journal, 6(5). https:\\\/\\\/doi.org\\\/10.53796\\\/hnsj65\\\/31&quot;,&quot;Chicago&quot;:&quot;Lashhab Raja Amhamed Ali, Sati Faraj Saleh, Al-Amruni Abdulbasit Abdullah, Al-Khafifi Faiza Faraj, Mami Ahmed Mohammed. 2025. \\&quot;In using Penalized Regression Models to solve the Multicollinearity and Multidimensional Problem.\\&quot; Humanities &amp; Natural Sciences Journal 6, no. 5. https:\\\/\\\/doi.org\\\/10.53796\\\/hnsj65\\\/31&quot;,&quot;Harvard&quot;:&quot;Lashhab R. A. A, Sati F. S, Al-Amruni A. A, Al-Khafifi F. F, Mami A. M. 2025. In using Penalized Regression Models to solve the Multicollinearity and Multidimensional Problem. Humanities &amp; Natural Sciences Journal. [Internet] 2025-05-01. [Cited 2026-05-11]. 6(5). Available at: https:\\\/\\\/www.hnjournal.net\\\/ar\\\/6-5-31\\\/. https:\\\/\\\/doi.org\\\/10.53796\\\/hnsj65\\\/31&quot;,&quot;Vancouver&quot;:&quot;Lashhab R. A. A, Sati F. S, Al-Amruni A. A, Al-Khafifi F. F, Mami A. M. In using Penalized Regression Models to solve the Multicollinearity and Multidimensional Problem. Humanities &amp; Natural Sciences Journal. [Internet]. 2025-05-01; 6(5). Available from: https:\\\/\\\/doi.org\\\/10.53796\\\/hnsj65\\\/31&quot;,&quot;IEEE&quot;:&quot;Lashhab R. A. A, Sati F. S, Al-Amruni A. A, Al-Khafifi F. F, Mami A. M, \\&quot;In using Penalized Regression Models to solve the Multicollinearity and Multidimensional Problem,\\&quot; Humanities &amp; Natural Sciences Journal, vol. 6, no. 5, 2025. https:\\\/\\\/doi.org\\\/10.53796\\\/hnsj65\\\/31&quot;,&quot;MLA&quot;:&quot;Lashhab Raja Amhamed Ali, Sati Faraj Saleh, Al-Amruni Abdulbasit Abdullah, Al-Khafifi Faiza Faraj, Mami Ahmed Mohammed. \\&quot;In using Penalized Regression Models to solve the Multicollinearity and Multidimensional Problem.\\&quot; Humanities &amp; Natural Sciences Journal, vol. 6, no. 5, 2025-05-01, https:\\\/\\\/doi.org\\\/10.53796\\\/hnsj65\\\/31&quot;}' data-cit-ar='{&quot;APA&quot;:&quot;\u0644\u0634\u0647\u0628 \u0631. \u0623. \u0639\u060c \u0633\u0627\u0637\u064a \u0641. \u0635\u060c \u0627\u0644\u0639\u0645\u0631\u0648\u0646\u064a \u0639. \u0639\u060c \u0627\u0644\u062e\u0641\u064a\u0641\u064a \u0641. \u0641\u060c \u0645\u0627\u0645\u064a \u0623. \u0645. (2025). \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0646\u0645\u0627\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062c\u0632\u0627\u0626\u064a\u0629 \u0644\u062d\u0644 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a \u0648\u062a\u0639\u062f\u062f \u0627\u0644\u0627\u0628\u0639\u0627\u062f. \u0645\u062c\u0644\u0629 \u0627\u0644\u0639\u0644\u0648\u0645 \u0627\u0644\u0627\u0646\u0633\u0627\u0646\u064a\u0629 \u0648\u0627\u0644\u0637\u0628\u064a\u0639\u064a\u0629\u060c 6(5). https:\\\/\\\/doi.org\\\/10.53796\\\/hnsj65\\\/31&quot;,&quot;Chicago&quot;:&quot;\u0644\u0634\u0647\u0628 \u0631\u062c\u0627\u0621 \u0623\u0645\u062d\u0645\u062f \u0639\u0644\u0649\u060c \u0633\u0627\u0637\u064a \u0641\u0631\u062c \u0635\u0627\u0644\u062d\u060c \u0627\u0644\u0639\u0645\u0631\u0648\u0646\u064a \u0639\u0628\u062f\u0627\u0644\u0628\u0627\u0633\u0637 \u0639\u0628\u062f\u0627\u0644\u0644\u0647\u060c \u0627\u0644\u062e\u0641\u064a\u0641\u064a \u0641\u0627\u064a\u0632\u0629 \u0641\u0631\u062c\u060c \u0645\u0627\u0645\u064a \u0623\u062d\u0645\u062f \u0645\u062d\u0645\u062f. 2025. \u00ab\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0646\u0645\u0627\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062c\u0632\u0627\u0626\u064a\u0629 \u0644\u062d\u0644 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a \u0648\u062a\u0639\u062f\u062f \u0627\u0644\u0627\u0628\u0639\u0627\u062f\u00bb. \u0645\u062c\u0644\u0629 \u0627\u0644\u0639\u0644\u0648\u0645 \u0627\u0644\u0627\u0646\u0633\u0627\u0646\u064a\u0629 \u0648\u0627\u0644\u0637\u0628\u064a\u0639\u064a\u0629\u060c 6(5). https:\\\/\\\/doi.org\\\/10.53796\\\/hnsj65\\\/31&quot;,&quot;Harvard&quot;:&quot;\u0644\u0634\u0647\u0628 \u0631. \u0623. \u0639\u060c \u0633\u0627\u0637\u064a \u0641. \u0635\u060c \u0627\u0644\u0639\u0645\u0631\u0648\u0646\u064a \u0639. \u0639\u060c \u0627\u0644\u062e\u0641\u064a\u0641\u064a \u0641. \u0641\u060c \u0645\u0627\u0645\u064a \u0623. \u0645. \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0646\u0645\u0627\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062c\u0632\u0627\u0626\u064a\u0629 \u0644\u062d\u0644 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a \u0648\u062a\u0639\u062f\u062f \u0627\u0644\u0627\u0628\u0639\u0627\u062f. \u0645\u062c\u0644\u0629 \u0627\u0644\u0639\u0644\u0648\u0645 \u0627\u0644\u0627\u0646\u0633\u0627\u0646\u064a\u0629 \u0648\u0627\u0644\u0637\u0628\u064a\u0639\u064a\u0629. [\u0627\u0646\u062a\u0631\u0646\u062a] 2025-05-01. 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\u0648\u062a\u0639\u062f\u062f \u0627\u0644\u0627\u0628\u0639\u0627\u062f\u00bb. \u0645\u062c\u0644\u0629 \u0627\u0644\u0639\u0644\u0648\u0645 \u0627\u0644\u0627\u0646\u0633\u0627\u0646\u064a\u0629 \u0648\u0627\u0644\u0637\u0628\u064a\u0639\u064a\u0629\u060c \u0645 6\u060c \u0639 5\u060c 2025-05-01\u060c https:\\\/\\\/doi.org\\\/10.53796\\\/hnsj65\\\/31&quot;}'>\r\n    <div class='hnsj-modal-header'>\r\n    <div class='hnsj-modal-title'>Cite \/ \u0627\u0644\u0627\u0633\u062a\u0634\u0647\u0627\u062f<\/div>\r\n    <button class='hnsj-modal-close' type='button' data-hnsj-close aria-label='Close'>\u00d7<\/button>\r\n    <\/div>\r\n\r\n    <div class='hnsj-tabs'>\r\n      <button type='button' class='hnsj-tab active' data-lang='en'>English (Roman)<\/button>\r\n      <button type='button' class='hnsj-tab' data-lang='ar'>\u0627\u0644\u0639\u0631\u0628\u064a\u0629<\/button>\r\n    <\/div>\r\n\r\n    <div class='hnsj-modal-body'>\r\n      <div class='hnsj-row'>\r\n        <button type='button' class='hnsj-copy' data-hnsj-copy>Copy<\/button>\r\n        <select class='hnsj-select' data-hnsj-style><\/select>\r\n        <\/div>\r\n\r\n      <textarea class='hnsj-textarea' data-hnsj-box readonly><\/textarea>\r\n\r\n      <div class='hnsj-actions'>\r\n        <div style='display:flex; gap:10px; flex-wrap:wrap;'>\r\n          <button type='button' class='hnsj-dl' data-hnsj-dl='ris'>Download RIS<\/button>\r\n          <button type='button' class='hnsj-dl' data-hnsj-dl='bib'>Download BibTeX<\/button>\r\n        <\/div>\r\n      <\/div>\r\n    <\/div>\r\n  <\/div>\r\n<\/div>\r\n<p style='text-align:justify; direction:rtl;'><strong>\u0627\u0644\u0645\u0633\u062a\u062e\u0644\u0635: <\/strong> \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0628\u062d\u062b\u060c \u0633\u0648\u0641 \u0646\u062a\u0646\u0627\u0648\u0644 \u0625\u062d\u062f\u0649 \u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u062a\u0642\u062f\u064a\u0631 \u0639\u0646\u062f \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 \u0627\u0644\u0627\u0639\u062a\u064a\u0627\u062f\u064a\u0629 \u0648\u0647\u064a \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a. \u0627\u0644\u062a\u064a \u062a\u0634\u064a\u0631 \u0625\u0644\u0649 \u0648\u062c\u0648\u062f \u0627\u0631\u062a\u0628\u0627\u0637\u0627\u062a \u0642\u0648\u064a\u0629 \u0628\u064a\u0646 \u0628\u0639\u0636 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u062a\u0641\u0633\u064a\u0631\u064a\u0629 \u0648\u0639\u0646\u062f \u0630\u0644\u0643 \u0641\u0625\u0646 \u062a\u0642\u062f\u064a\u0631 \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u0633\u064a\u0643\u0648\u0646 \u0645\u0636\u0644\u0644\u0627\u064b. \u0646\u0642\u062a\u0631\u062d \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0628\u062d\u062b \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0627 \u064a\u0633\u0645\u064a \u0646\u0645\u0627\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062c\u0632\u0627\u0626\u064a\u0629 (Penalized Regression Models) \u0648\u0630\u0644\u0643 \u0644\u062d\u0644 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a \u0639\u0646 \u0637\u0631\u064a\u0642 \u062a\u0642\u0644\u064a\u0644 \u062e\u0637\u0648\u0631\u0629 \u0647\u0630\u0647 \u0627\u0644\u0638\u0627\u0647\u0631\u0629\u060c \u0648\u0647\u0630\u0627 \u0639\u0644\u0649 \u062d\u0633\u0627\u0628 \u0627\u0646\u062d\u064a\u0627\u0632 \u0642\u064a\u0645 \u0627\u0644\u062a\u0642\u062f\u064a\u0631\u0627\u062a. \u064a\u0647\u062f\u0641 \u0627\u0644\u0628\u062d\u062b \u0627\u0644\u064a \u0645\u0642\u0627\u0631\u0646\u0629 \u0643\u0641\u0627\u0621\u0629 \u062a\u0642\u062f\u064a\u0631 \u0645\u0639\u0627\u0644\u0645 \u0646\u0645\u0648\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062e\u0637\u064a \u0627\u0644\u0645\u062a\u0639\u062f\u062f \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062e\u0645\u0633\u0629 \u0645\u0646 \u0646\u0645\u0627\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062c\u0632\u0627\u0626\u064a\u0629 Penalized Regression Models \u0648\u0647\u064a \u0643\u0627\u0644\u062a\u0627\u0644\u064a: \u0646\u0645\u0648\u0630\u062c \u0627\u0646\u062d\u062f\u0627\u0631 Ridge\u060c \u0648\u0646\u0645\u0648\u0630\u062c \u0627\u0646\u062d\u062f\u0627\u0631 Lasso\u060c \u0648\u0646\u0645\u0648\u0630\u062c \u0627\u0646\u062d\u062f\u0627\u0631 Elastic net\u060c \u0648\u0646\u0645\u0648\u0630\u062c \u0627\u0646\u062d\u062f\u0627\u0631 Lasso Adaptive\u060c \u0648\u0646\u0645\u0648\u0630\u062c  \u0627\u0646\u062d\u062f\u0627\u0631 Adaptive Elastic Net. \u0646\u0633\u062a\u062e\u062f\u0645 \u0647\u0630\u0627 \u0627\u0644\u0628\u062d\u062b \u0646\u0645\u0648\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062e\u0637\u064a \u0627\u0644\u0645\u062a\u0639\u062f\u062f\u060c \u0648\u0627\u0644\u0630\u064a \u064a\u062a\u0643\u0648\u0646 \u0645\u0646 \u0645\u062a\u063a\u064a\u0631 \u062a\u0627\u0628\u0639 \u0648\u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u062a\u0648\u0636\u064a\u062d\u064a\u0629 \u0641\u064a \u062d\u0627\u0644\u0629 \u0643\u0627\u0646 \u0647\u0646\u0627\u0643 \u0648\u062c\u0648\u062f \u0644\u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a \u0648\u0643\u0630\u0644\u0643 \u0643\u0627\u0646 \u0639\u062f\u062f \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0642\u0644\u0629 \u0623\u0643\u0628\u0631 \u0645\u0646 \u062d\u062c\u0645 \u0639\u064a\u0646\u0629 \u0627\u0644\u062f\u0631\u0627\u0633\u0629 \u062a\u0633\u0645\u0649 \u0647\u0630\u0647 \u0627\u0644\u0638\u0627\u0647\u0631\u0629 \"\u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0639\u0627\u0644\u064a\u0629 \u0627\u0644\u0623\u0628\u0639\u0627\u062f\". \u0644\u0644\u0645\u0642\u0627\u0631\u0646\u0629 \u0628\u064a\u0646 \u0643\u0641\u0627\u0621\u0629 \u0646\u0645\u0627\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062c\u0632\u0627\u0626\u064a\u0629\u060c \u064a\u062a\u0645 \u0627\u0644\u0627\u0639\u062a\u0645\u0627\u062f \u0639\u0644\u0649 \u0645\u0639\u064a\u0627\u0631 \u0645\u062a\u0648\u0633\u0637 \u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0623\u062e\u0637\u0627\u0621 (MSE). \u062a\u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0633\u0644\u0648\u0628 \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0628\u062d\u062b \u0639\u0644\u0649 \u0628\u064a\u0627\u0646\u0627\u062a \u0645\u0648\u0644\u062f\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0623\u0648\u0644\u0627 \u0623\u062d\u062c\u0627\u0645 \u0627\u0644\u0639\u064a\u0646\u0627\u062a \u0627\u0644\u0635\u063a\u064a\u0631\u0629 \u062b\u0627\u0646\u064a\u0627 \u0623\u062d\u062c\u0627\u0645 \u0627\u0644\u0639\u064a\u0646\u0629 \u0627\u0644\u0645\u062a\u0648\u0633\u0637\u0629 \u062b\u0627\u0644\u062b\u0627 \u0623\u062d\u062c\u0627\u0645 \u0627\u0644\u0639\u064a\u0646\u0627\u062a \u0627\u0644\u0643\u0628\u064a\u0631\u0629\u060c \u0648\u064a\u062a\u0645 \u062a\u062d\u062f\u064a\u062f \u0639\u062f\u062f \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0642\u0644\u0629 \u0628\u062d\u064a\u062b \u062a\u0643\u0648\u0646 \u0627\u0642\u0644 \u0645\u0646 \u062d\u062c\u0645 \u0627\u0644\u0639\u064a\u0646\u0629. \u0648\u064a\u062a\u0645 \u062a\u0648\u0644\u064a\u062f \u062d\u062f \u0627\u0644\u062e\u0637\u0623 \u0645\u0631\u0629 \u0645\u0646 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a\u060c \u0648 \u0645\u0631\u0629 \u0645\u0646 \u062a\u0648\u0632\u064a\u0639 t(3).  \u064a\u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0641\u064a \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062a\u0643\u062a\u064a\u0643 \u0645\u0648\u0646\u062a \u0643\u0627\u0631\u0644\u0648 \u0645\u0639 1000 \u062a\u0643\u0631\u0627\u0631 \u0644\u0643\u0644 \u062d\u0627\u0644\u0629. \u0648\u062a\u0648\u0635\u0644\u0646\u0627 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0627\u0644\u064a \u0623\u0646 \u0646\u0645\u0627\u0630\u062c \u0627\u0646\u062d\u062f\u0627\u0631 Adaptive Elastic net \u062a\u062a\u062d\u0635\u0644 \u0639\u0644\u0649 \u0627\u0641\u0636\u0644\u064a\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0645\u0639\u064a\u0627\u0631 \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u062f\u0646\u0649 \u0644\u0645\u062a\u0648\u0633\u0637 \u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u062e\u0637\u0623 \u0641\u064a \u062c\u0645\u064a\u0639 \u0627\u0644\u062d\u0627\u0644\u0627\u062a.<\/p><p style='text-align:right;'><strong>\u0627\u0644\u0643\u0644\u0645\u0627\u062a \u0627\u0644\u0645\u0641\u062a\u0627\u062d\u064a\u0629: <\/strong> \u0646\u0645\u0627\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062c\u0632\u0627\u0626\u064a\u0629 Penalized Regression Models\u060c \u0646\u0645\u0648\u0630\u062c \u0627\u0646\u062d\u062f\u0627\u0631 Ridge\u060c \u0646\u0645\u0648\u0630\u062c \u0627\u0646\u062d\u062f\u0627\u0631 Lasso\u060c \u0646\u0645\u0648\u0630\u062c \u0627\u0646\u062d\u062f\u0627\u0631 Elastic net\u060c \u0646\u0645\u0648\u0630\u062c \u0627\u0646\u062d\u062f\u0627\u0631 Lasso Adaptive\u060c \u0646\u0645\u0648\u0630\u062c \u0627\u0646\u062d\u062f\u0627\u0631 Adaptive Elastic Net.<\/p><p style='text-align:justify; direction:ltr;'><strong>Abstract: <\/strong> The goal of this thesis is to compare the efficiency of feature estimation of the multiple linear regression model using the analysis of the penalized regression models on five estimators, which are the Ridge regression model, the lasso regression model, the Elastic net regression model, the adaptive lasso regression model, and the Adaptive Elastic Net regression model. This research uses a multiple linear regression model, which consists of a dependent variable and a set of independent variables. If the number of independent variables is greater than the number of sample sizes it is called high dimensional data. To compare the efficiency of the five proposed estimators, the criterion is based on mean square errors (MSE). The simulation study is conducted on data generated in this research through small sample sizes, medium sample sizes, and large sample sizes, the number of independent variables is set to less than the sample size. The independent variables are generated from the normal distribution, and the error term is generated once from the normal distribution, and once from the non-normal distribution (heavy-tailed t distribution). The data are obtained through Monte Carlo simulation with 1000 iterations for each case. The results found that the Adaptive Elastic net regression models get the advantage by the minimum mean square error (MSE) criterion in all cases.<\/p><p style='direction:ltr; text-align:left;'><strong>Keywords: <\/strong> Penalized Regression Models, Ridge Regression, Lasso, Elastic net estimator, Lasso Adaptive, and Adaptive Elastic Net.<\/p><\/div>\n\n\n<ol>\n<li style=\"text-align: justify;\"><strong>\u0645\u0642\u062f\u0645\u0629 \u0641\u064a \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631<\/strong><\/li>\n<\/ol>\n<p style=\"text-align: justify;\">\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0647\u0648 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u0625\u062d\u0635\u0627\u0626\u064a\u0629 \u0644\u062f\u0631\u0627\u0633\u0629 \u0647\u0630\u0647 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0628\u064a\u0646 \u0645\u062a\u063a\u064a\u0631\u064a\u0646 \u0623\u062d\u062f\u0647\u0645\u0627 \u0645\u0633\u062a\u0642\u0644 \u0648\u0627\u0644\u0627\u062e\u0631 \u062a\u0627\u0628\u0639. \u064a\u0639\u062a\u0628\u0631 \u0627\u0644\u0634\u0643\u0644 \u0627\u0644\u0623\u0648\u0644\u064a \u0644\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062e\u0637\u064a \u0647\u0648 \u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 \u0627\u0644\u062a\u064a \u0646\u0634\u0631\u0647\u0627 Legendre \u0641\u064a \u0639\u0627\u0645 1805\u060c \u0648 Gauss \u0641\u064a \u0639\u0627\u0645 1809. \u0642\u062f \u062a\u0639\u0648\u062f \u0643\u0644\u0645\u0629 &#8220;\u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631&#8221; \u0648\u0637\u0631\u0642 \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0628\u064a\u0646 \u0645\u062a\u063a\u064a\u0631\u064a\u0646 \u0625\u0644\u0649 \u062d\u0648\u0627\u0644\u064a 100 \u0639\u0627\u0645 \u0645\u0636\u062a. \u0648\u0642\u062f \u062a\u0645 \u062a\u0642\u062f\u064a\u0645\u0647 \u0644\u0623\u0648\u0644 \u0645\u0631\u0629 \u0645\u0646 \u0642\u0628\u0644 Francis Galton \u0641\u064a \u0639\u0627\u0645 1886 (Bates and Watts, 1988).<\/p>\n<p style=\"text-align: justify;\">\u064a\u062a\u0637\u0644\u0628 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062e\u0637\u064a \u0623\u0646 \u064a\u0643\u0648\u0646 \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u062e\u0637\u064a\u064b\u0627 \u0641\u064a \u0645\u0639\u0627\u0644\u0645 \u0646\u0645\u0648\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631. \u0648\u064a\u0634\u0627\u0631 \u0625\u0644\u0649 \u062a\u0642\u062f\u064a\u0631 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 \u0628\u0646\u0627\u0621\u064b \u0639\u0644\u0649 \u0647\u0630\u0647 \u0627\u0644\u0627\u0641\u062a\u0631\u0627\u0636\u0627\u062a \u0628\u0627\u0633\u0645 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 \u0627\u0644\u0639\u0627\u062f\u064a\u0629. \u0641\u064a \u062d\u064a\u0646 \u0623\u0646 \u0627\u0641\u062a\u0631\u0627\u0636\u0627\u062a \u0627\u0644\u0627\u0633\u062a\u0642\u0644\u0627\u0644 \u0648\u0627\u0644\u062a\u0628\u0627\u064a\u0646 \u0627\u0644\u0645\u0634\u062a\u0631\u0643 \u0635\u062d\u064a\u062d\u0629\u060c \u0641\u0625\u0646 \u0645\u0642\u062f\u0631\u0627\u062a \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 \u0644\u0647\u0627 \u0627\u0644\u062e\u0627\u0635\u064a\u0629 \u0627\u0644\u0645\u0631\u063a\u0648\u0628\u0629 \u0644\u0643\u0648\u0646\u0647\u0627 \u0623\u0641\u0636\u0644 \u0645\u0642\u062f\u0631 \u062e\u0637\u064a \u063a\u064a\u0631 \u0645\u062a\u062d\u064a\u0632 (Best Linear Unbiased Estimator (BLUE)) \u0645\u0639 \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u062f\u0646\u0649 \u0645\u0646 \u0627\u0644\u062a\u0628\u0627\u064a\u0646 \u0628\u064a\u0646 \u062c\u0645\u064a\u0639 \u0627\u0644\u0645\u0642\u062f\u0631\u064a\u0646 \u0627\u0644\u062e\u0637\u064a\u064a\u0646 \u063a\u064a\u0631 \u0627\u0644\u0645\u062a\u062d\u064a\u0632\u064a\u0646 \u0627\u0644\u0645\u062d\u062a\u0645\u0644\u064a\u0646. \u0639\u0646\u062f \u0627\u0633\u062a\u064a\u0641\u0627\u0621 \u0627\u0641\u062a\u0631\u0627\u0636 \u0627\u0644\u062a\u0628\u0639\u064a\u0629 \u0644\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a \u0644\u0644\u0627\u062e\u0637\u0627\u0621\u060c \u0641\u0625\u0646 \u0645\u0642\u062f\u0631\u0627\u062a \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 \u062a\u0639\u0627\u062f\u0644 \u0645\u0642\u062f\u0631\u0627\u062a \u0627\u0644\u062a\u0642\u062f\u064a\u0631 \u0628\u0648\u0627\u0633\u0637\u0629 \u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u0627\u0645\u0643\u0627\u0646 \u0627\u0644\u0627\u0639\u0638\u0645 (Agresti, 2002).<\/p>\n<p style=\"text-align: justify;\">\u0623\u0631\u0628\u0639\u0629 \u0645\u0646 \u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u0631\u0626\u064a\u0633\u064a\u0629 \u0641\u064a \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 \u062a\u062a\u0639\u0644\u0642 \u0628\u0641\u0634\u0644 \u0627\u0644\u0627\u0641\u062a\u0631\u0627\u0636\u0627\u062a \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629\u060c \u0648\u0647\u064a: \u0645\u0634\u0643\u0644\u0629 \u0639\u062f\u0645 \u0627\u0644\u062a\u0628\u0639\u064a\u0629 \u0627\u0644\u0627\u062e\u0637\u0627\u0621 \u0644\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a (Non-normality Problem)\u060c \u0645\u0634\u0643\u0644\u0629 \u0639\u062f\u0645 \u062a\u062c\u0627\u0646\u0633 \u0627\u0644\u062a\u0628\u0627\u064a\u0646 (Heterogeneous Variances Problem)\u060c \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0627\u0631\u062a\u0628\u0627\u0637 \u0627\u0644\u0630\u0627\u062a\u064a (Correlated Errors Problem)\u060c \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a ( Multi-Col-linearity Problem) (Baltagi, 2001).<\/p>\n<p style=\"text-align: justify;\"><strong>1.1 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a <\/strong><\/p>\n<p style=\"text-align: justify;\">\u0645\u0635\u0641\u0648\u0641\u0629 X \u0627\u0644\u062a\u064a \u062a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u062a\u0648\u0636\u064a\u062d\u064a\u0629 \u0642\u062f \u062a\u0646\u062a\u062c \u0639\u0646\u062f \u0627\u062c\u0631\u0627\u0621 \u0639\u0645\u0644\u064a\u0629 \u062d\u0633\u0627\u0628\u064a\u0629 \u0639\u0644\u064a\u0647\u0627 \u0642\u064a\u0645 \u0645\u0641\u0631\u062f\u0629 (Singularity). \u064a\u062d\u062f\u062b \u0647\u0630\u0627 \u0639\u0646\u062f\u0645\u0627 \u062a\u0643\u0648\u0646 \u0628\u0639\u0636 \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0627\u0644\u062e\u0637\u064a\u0629 \u0644\u0623\u0639\u0645\u062f\u0629 X \u0645\u0633\u0627\u0648\u064a\u0629 \u062a\u0645\u0627\u0645\u064b\u0627 \u0644\u0644\u0635\u0641\u0631. \u064a\u0635\u0628\u062d \u0627\u0644\u0623\u0645\u0631 \u0623\u0643\u062b\u0631 \u0648\u0636\u0648\u062d\u064b\u0627 \u0639\u0646\u062f\u0645\u0627 \u064a\u062a\u0645 \u062d\u0633\u0627\u0628 \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 \u0644\u0623\u0646 \u0627\u0644\u062d\u0644 \u0627\u0644\u0641\u0631\u064a\u062f \u0644\u0640 \u063a\u064a\u0631 \u0645\u0648\u062c\u0648\u062f. \u062a\u064f\u0639\u0631\u0641 \u0627\u0644\u0635\u0639\u0648\u0628\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u0646\u0634\u0623 \u0645\u0646 \u0643\u0648\u0646 X \u0645\u0641\u0631\u062f\u064b\u0627 \u062a\u0642\u0631\u064a\u0628\u064b\u0627 \u0628\u0627\u0633\u0645 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a.<\/p>\n<p style=\"text-align: justify;\"><strong>2.1 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a \u0641\u064a \u0646\u0645\u0627\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062e\u0637\u064a<\/strong><\/p>\n<p style=\"text-align: justify;\">\u062a\u0630\u0643\u0631 \u0623\u0646 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a \u0641\u064a \u0646\u0645\u0627\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062e\u0637\u064a \u062a\u0646\u0634\u0623 \u0639\u0646\u062f\u0645\u0627 \u062a\u0643\u0648\u0646 \u0645\u062c\u0645\u0648\u0639\u0629 \u062e\u0637\u064a\u0629 \u0648\u0627\u062d\u062f\u0629 \u0639\u0644\u0649 \u0627\u0644\u0623\u0642\u0644 \u0645\u0646 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u062a\u0648\u0636\u064a\u062d\u064a\u0629 \u062a\u0633\u0627\u0648\u064a \u0627\u0644\u0635\u0641\u0631 \u062a\u0642\u0631\u064a\u0628\u064b\u0627. \u0647\u0646\u0627\u0643 \u0639\u062f\u0629 \u0637\u0631\u0642 \u0644\u0638\u0647\u0648\u0631 \u0627\u0644\u062a\u0641\u0631\u062f \u0627\u0644\u0642\u0631\u064a\u0628 (near-singularity) :<\/p>\n<p style=\"text-align: justify;\">1. \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0627\u0644\u0633\u064a\u0626 \u0627\u0644\u0630\u064a \u064a\u0636\u0639 \u0642\u064a\u0648\u062f\u064b\u0627 \u0639\u0644\u0649 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u062a\u0648\u0636\u064a\u062d\u064a\u0629 \u0627\u0644\u062a\u064a \u0628\u062f\u0648\u0631\u0647\u0627 \u062a\u062c\u0628\u0631 \u0639\u0644\u0649 \u0627\u0644\u0627\u0644\u062a\u0632\u0627\u0645 \u0628\u0647\u0627 \u0623\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u062b\u0627\u0628\u062a \u0633\u064a\u0624\u062f\u064a \u062d\u062a\u0645\u0627 \u0625\u0644\u0649 \u0625\u0646\u0634\u0627\u0621 \u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u062a\u0639\u062f\u062f \u062e\u0637\u064a.<\/p>\n<p style=\"text-align: justify;\">2. \u0642\u062f \u062a\u0638\u0647\u0631 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u062a\u0648\u0636\u064a\u062d\u064a\u0629 \u0644\u0644\u062a\u0637\u0628\u064a\u0642 \u062a\u0628\u0639\u064a\u0629 \u0634\u0628\u0647 \u062e\u0637\u064a\u0629 \u0628\u0633\u0628\u0628 \u0627\u0644\u0642\u064a\u0648\u062f \u0627\u0644\u0628\u064a\u0648\u0644\u0648\u062c\u064a\u0629 \u0623\u0648 \u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0626\u064a\u0629 \u0623\u0648 \u0627\u0644\u0643\u064a\u0645\u064a\u0627\u0626\u064a\u0629.<\/p>\n<p style=\"text-align: justify;\">3. \u0642\u062f \u064a\u0624\u062f\u064a \u0639\u062f\u0645 \u0643\u0641\u0627\u064a\u0629 \u062d\u062c\u0645 \u0627\u0644\u0639\u064a\u0646\u0629 \u0625\u0644\u0649 \u0625\u0646\u0634\u0627\u0621 \u0628\u064a\u0627\u0646\u0627\u062a \u062a\u0643\u0648\u0646 \u0641\u064a\u0647\u0627 \u0627\u0644\u062a\u0628\u0639\u064a\u0629 \u0634\u0628\u0647 \u0627\u0644\u062e\u0637\u064a\u0629 \u0646\u062a\u064a\u062c\u0629 \u0644\u0639\u0645\u0644\u064a\u0629 \u062c\u0645\u0639 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a (. (Yan and Su, 2005<\/p>\n<p style=\"text-align: justify;\">\u0644\u064a\u0633 \u0645\u0646 \u0627\u0644\u0633\u0647\u0644 \u062a\u062d\u062f\u064a\u062f \u0623\u0635\u0644 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a \u0628\u0648\u0636\u0648\u062d \u0648\u0644\u0643\u0646 \u0645\u0646 \u0627\u0644\u0645\u0647\u0645 \u0644\u0644\u063a\u0627\u064a\u0629 \u0641\u0647\u0645 \u0637\u0628\u064a\u0639\u062a\u0647\u0627 \u0642\u062f\u0631 \u0627\u0644\u0625\u0645\u0643\u0627\u0646. \u0628\u0639\u062f \u0645\u0639\u0631\u0641\u0629 \u0637\u0628\u064a\u0639\u0629 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a\u060c \u0633\u064a\u0633\u0627\u0639\u062f\u0646\u0627 \u062f\u0627\u0626\u0645\u064b\u0627 \u062a\u062d\u062f\u064a\u062f \u0645\u0635\u062f\u0631\u0647\u0627\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0627\u0644\u0637\u0631\u0642 \u0627\u0644\u0645\u0646\u0627\u0633\u0628\u0629 \u0644\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0627\u0644\u0645\u0634\u0643\u0644\u0629 \u0648\u062a\u0641\u0633\u064a\u0631 \u0646\u062a\u0627\u0626\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631.<\/p>\n<p style=\"text-align: justify;\"><strong>1.2.1 \u0645\u0642\u062f\u0645\u0629 \u0625\u0644\u0649 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u062a\u062d\u064a\u0632<\/strong><\/p>\n<p style=\"text-align: justify;\">\u0648\u0645\u0646 \u0627\u0644\u0645\u0639\u0631\u0648\u0641 \u0623\u0646 \u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062a\u064a \u064a\u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647\u0627 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 \u0627\u0644\u0627\u0639\u062a\u064a\u0627\u062f\u064a\u0629 \u0647\u064a \u0623\u0641\u0636\u0644 \u0627\u0644\u0645\u0642\u062f\u0631\u0627\u062a \u0627\u0644\u062e\u0637\u064a\u0629 \u0627\u0644\u063a\u064a\u0631 \u0627\u0644\u0645\u062a\u062d\u064a\u0632\u0629 (BLUE). \u0639\u0644\u0649 \u0648\u062c\u0647 \u0627\u0644\u062f\u0642\u0629\u060c \u0641\u0625\u0646 \u0645\u0642\u062f\u0631\u0627\u062a \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 \u0644\u062f\u064a\u0647\u0627 \u0623\u0635\u063a\u0631 \u062a\u0628\u0627\u064a\u0646 \u0628\u064a\u0646 \u062c\u0645\u064a\u0639 \u0627\u0644\u0645\u0642\u062f\u0631\u0627\u062a \u0627\u0644\u0645\u062d\u062a\u0645\u0644\u0629 \u0627\u0644\u062a\u064a \u062a\u0645\u062b\u0644 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u062e\u0637\u064a\u0629 \u0644\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0648\u063a\u064a\u0631 \u0645\u062a\u062d\u064a\u0632\u0629 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0645\u0639\u0627\u0644\u0645 \u0627\u0644\u062a\u064a \u064a\u062a\u0645 \u062a\u0642\u062f\u064a\u0631\u0647\u0627. \u064a\u0639\u062a\u0628\u0631 \u0645\u062a\u0648\u0633\u0637 \u0645\u0631\u0628\u0639 \u0627\u0644\u062e\u0637\u0623 (MSE) \u0623\u0641\u0636\u0644 \u0645\u0642\u064a\u0627\u0633 \u0644\u062d\u0633\u0627\u0628 \u0645\u062a\u0648\u0633\u0637 &#8220;\u0645\u062f\u064a \u0642\u0631\u0628&#8221; \u0627\u0644\u0645\u0642\u062f\u0631 \u0645\u0646 \u0627\u0644\u0645\u0639\u0644\u0645\u0629 \u0627\u0644\u062a\u064a \u064a\u062a\u0645 \u062a\u0642\u062f\u064a\u0631\u0647\u0627.<\/p>\n<p style=\"text-align: justify;\">\u0625\u0630\u0627 \u0643\u0627\u0646 \u0645\u0642\u062f\u0631\u064b\u0627 \u0645\u062a\u062d\u064a\u0632\u064b\u0627 \u064a\u0645\u0644\u0643 \u0645\u062a\u0648\u0633\u0637 \u0645\u0631\u0628\u0639 \u062e\u0637\u0623 \u0623\u0635\u063a\u0631 \u0645\u0646 \u0627\u0644\u0645\u0642\u062f\u0631 \u063a\u064a\u0631 \u0627\u0644\u0645\u062a\u062d\u064a\u0632 \ud835\udf03\u060c \u0641\u064a\u0645\u0643\u0646 \u062a\u0639\u0631\u064a\u0641 \u0645\u062a\u0648\u0633\u0637 \u0645\u0631\u0628\u0639 \u0627\u0644\u062e\u0637\u0623 \u0644\u0640 \u0639\u0644\u0649 \u0627\u0644\u0646\u062d\u0648 \u0627\u0644\u062a\u0627\u0644\u064a<\/p>\n<p style=\"text-align: justify;\">(1) () MSE=<\/p>\n<p style=\"text-align: justify;\">\u062a\u0630\u0643\u0631 \u0623\u0646 \u062a\u0628\u0627\u064a\u0646 \u0627\u0644\u0645\u0642\u062f\u0631 \u064a\u0645\u0643\u0646 \u0623\u064a\u0636\u064b\u0627 \u062a\u0639\u0631\u064a\u0641\u0647 \u0639\u0644\u0649 \u0623\u0646\u0647<\/p>\n<p style=\"text-align: justify;\">Var ( = (2)<\/p>\n<p style=\"text-align: justify;\">\u0648\u0647\u0630\u0627 \u064a\u0639\u0646\u064a \u0623\u0646 \u0645\u062a\u0648\u0633\u0637 \u0645\u0631\u0628\u0639 \u0627\u0644\u062e\u0637\u0623 (MSE) \u064a\u0642\u0648\u0645 \u0628\u062d\u0633\u0627\u0628 \u0645\u062a\u0648\u0633\u0637 \u0627\u0644\u0627\u0646\u062d\u0631\u0627\u0641 \u0627\u0644\u0645\u0631\u0628\u0639 \u0644\u0644\u0645\u0642\u062f\u0631 \u0639\u0646 \u0627\u0644\u0645\u0639\u0644\u0645\u0629 \u0627\u0644\u062a\u064a \u064a\u062a\u0645 \u062a\u0642\u062f\u064a\u0631\u0647\u0627\u060c \u0641\u064a \u062d\u064a\u0646 \u0623\u0646 \u0627\u0644\u062a\u0628\u0627\u064a\u0646 \u064a\u062d\u0633\u0628 \u0628\u0648\u0627\u0633\u0637\u0629 \u0645\u062a\u0648\u0633\u0637 \u0627\u0644\u0627\u0646\u062d\u0631\u0627\u0641 \u0627\u0644\u0645\u0631\u0628\u0639 \u0644\u0644\u0645\u0642\u062f\u0631 \u0639\u0646 \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0645\u062a\u0648\u0642\u0639\u0629 \u0644\u0647.<\/p>\n<p style=\"text-align: justify;\">\u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0645\u0642\u062f\u0631 \u063a\u064a\u0631 \u0645\u062a\u062d\u064a\u0632\u060c \u0641\u0625\u0646 E()=\u03b8 \u0648.MSE() =( \u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0645\u0642\u062f\u0631 \u0645\u062a\u062d\u064a\u0632\u064b\u0627\u060c \u0641\u0625\u0646 MSE \u062a\u0633\u0627\u0648\u064a \u062a\u0628\u0627\u064a\u0646 \u0627\u0644\u0645\u0642\u062f\u0631 \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0645\u0631\u0628\u0639 \u0627\u0646\u062d\u064a\u0627\u0632\u0647\u060c \u062d\u064a\u062b Bias () = . \u0645\u0646 \u0627\u0644\u0645\u0645\u0643\u0646 \u062c\u062f\u064b\u0627 \u0623\u0646 \u064a\u062d\u0635\u0644 \u0627\u0644\u0645\u0642\u062f\u0631 \u0627\u0644\u0645\u062a\u062d\u064a\u0632 \u0639\u0644\u0649 \u062a\u0628\u0627\u064a\u0646 \u0623\u0635\u063a\u0631 \u0628\u062f\u0631\u062c\u0629 \u0643\u0627\u0641\u064a\u0629 \u0645\u0646 \u062a\u0628\u0627\u064a\u0646 \u0627\u0644\u0645\u0642\u062f\u0631 \u063a\u064a\u0631 \u0627\u0644\u0645\u062a\u062d\u064a\u0632 \u0645\u0646 \u0623\u062c\u0644 \u0627\u0644\u062a\u0639\u0648\u064a\u0636 \u0639\u0646 \u0627\u0644\u062a\u062d\u064a\u0632 \u0627\u0644\u0645\u0642\u062f\u0645.<\/p>\n<p style=\"text-align: justify;\">\u0641\u064a \u0645\u062b\u0644 \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0627\u062a\u060c \u064a\u0643\u0648\u0646 \u0627\u0644\u0645\u0642\u062f\u0631 \u0627\u0644\u0645\u062a\u062d\u064a\u0632 \u0623\u0642\u0631\u0628 \u0641\u064a \u0627\u0644\u0645\u062a\u0648\u0633\u0637 \u0625\u0644\u0649 \u0627\u0644\u0645\u0639\u0644\u0645\u0629 \u0627\u0644\u0645\u0631\u0627\u062f \u062a\u0642\u062f\u064a\u0631\u0647\u0627 \u0645\u0646 \u0627\u0644\u0645\u0642\u062f\u0631 \u0627\u0644\u063a\u064a\u0631 \u0627\u0644\u0645\u062a\u062d\u064a\u0632. \u0648\u064a\u0645\u062b\u0644 \u0630\u0644\u0643 \u0627\u0644\u0627\u0633\u062a\u0631\u0627\u062a\u064a\u062c\u064a\u0629 \u0627\u0644\u0631\u0626\u064a\u0633\u064a\u0629 \u0644\u062a\u0643\u062a\u064a\u0643\u0627\u062a \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u062a\u062d\u064a\u0632 (Hoerl and Kennard, 1975).<\/p>\n<p style=\"text-align: justify;\">\u0627\u0644\u0634\u0643\u0644 (1) \u0631\u0633\u0645 \u062a\u0648\u0636\u064a\u062d\u064a \u0644\u062a\u0642\u062f\u064a\u0631 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u062a\u062d\u064a\u0632<\/p>\n<p style=\"text-align: justify;\">\u064a\u0633\u062a\u0639\u0631\u0636 \u0627\u0644\u0634\u0643\u0644 1 \u0627\u0644\u0645\u064a\u0632\u0627\u062a \u0627\u0644\u0645\u062d\u062a\u0645\u0644\u0629 \u0644\u0644\u0645\u0642\u062f\u0631\u064a\u0646 \u0627\u0644\u0645\u062a\u062d\u064a\u0632\u064a\u0646. \u064a\u062a\u0645 \u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a \u0644\u0645\u0642\u062f\u0631 \u063a\u064a\u0631 \u0645\u062a\u062d\u064a\u0632 \u03b8\u0303 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0645\u0639\u0644\u0645\u0629 \u0628\u0627\u0644\u0645\u0646\u062d\u0646\u0649 \u0627\u0644\u0639\u0627\u062f\u064a \u0627\u0644\u0645\u062a\u0645\u0631\u0643\u0632 \u0639\u0646\u062f E(\u03b8\u0303) . \u0644\u0627\u062d\u0638 \u0623\u0646 \u0627\u0644\u062a\u062d\u064a\u0632 \u0647\u0648 \u0627\u0644\u0641\u0631\u0642 \u0628\u064a\u0646 (E(\u03b8\u0303 \u0648\u03b8. \u0644\u0627\u062d\u0638 \u0623\u064a\u0636\u064b\u0627 \u0623\u0646 \u0627\u0644\u0641\u0627\u0631\u0642 \u0627\u0644\u0623\u0635\u063a\u0631 \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u064a\u0639\u0643\u0633 \u062a\u0628\u0627\u064a\u0646\u0647 \u0627\u0644\u0623\u0635\u063a\u0631. \u0648\u0644\u0630\u0644\u0643\u060c \u0642\u062f \u064a\u0643\u0648\u0646 \u0645\u0646 \u0627\u0644\u0645\u0645\u0643\u0646 \u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0645\u0642\u062f\u0631 \u064a\u0643\u0648\u0646 \u0645\u062c\u0645\u0648\u0639 \u0627\u0646\u062d\u064a\u0627\u0632\u0647 \u0627\u0644\u062a\u0631\u0628\u064a\u0639\u064a \u0648\u062a\u0628\u0627\u064a\u0646\u0647 (\u0623\u064a MSE) \u0623\u0635\u063a\u0631 \u0645\u0646 \u062a\u0628\u0627\u064a\u0646 \u0627\u0644\u0645\u0642\u062f\u0631 \u063a\u064a\u0631 \u0627\u0644\u0645\u062a\u062d\u064a\u0632.<\/p>\n<p style=\"text-align: justify;\"><strong>2.2.1 \u0627\u0644\u062f\u0631\u0627\u0633\u0627\u062a \u0627\u0644\u0633\u0627\u0628\u0642\u0629<\/strong><\/p>\n<p style=\"text-align: justify;\">\u062a\u0645 \u0627\u0642\u062a\u0631\u0627\u062d \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0637\u0631\u0642 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u062a\u062d\u064a\u0632\u0629 \u0643\u062d\u0644\u0648\u0644 \u0644\u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a. \u0627\u0646\u0643\u0645\u0627\u0634 Stein (Stein, 1960) \u0648\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0646\u0643\u0645\u0627\u0634 \u0631\u064a\u062f\u062c (Hoerl and Kennard, 1975) \u0648\u0645\u0634\u063a\u0644 \u0627\u0644\u0627\u0646\u0643\u0645\u0627\u0634 \u0648\u0627\u0644\u0627\u062e\u062a\u064a\u0627\u0631 \u0627\u0644\u0645\u0637\u0644\u0642 \u0627\u0644\u0623\u0642\u0644 (<strong>LASSO<\/strong>) \u0627\u0644\u0630\u064a \u0627\u0642\u062a\u0631\u062d\u0647 Tibshirani (1996)\u060c \u0648\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u0643\u0648\u0646\u0627\u062a \u0627\u0644\u0631\u0626\u064a\u0633\u064a\u0629 Hocking \u060c Speed \u060c \u0648 Lynn (1976)\u060c Marquardt (1970)\u060c \u0648 Webster \u060c Gunst \u060c \u0648 Mason (1974).<\/p>\n<p style=\"text-align: justify;\">\u0644\u0642\u062f \u062a\u0645 \u0642\u0628\u0648\u0644 \u0637\u0631\u0642 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u062a\u062d\u064a\u0632\u0629 \u0647\u0630\u0647 \u0639\u0627\u0644\u0645\u064a\u064b\u0627 \u0648\u0644\u0643\u0646 \u064a\u062c\u0628 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647\u0627 \u0628\u062d\u0630\u0631. \u064a\u0648\u0636\u062d \u0645\u0628\u0631\u0631 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0639\u064a\u0627\u0631 \u0645\u062a\u0648\u0633\u0637 \u0645\u0631\u0628\u0639 \u0627\u0644\u062e\u0637\u0623 (MSE) \u0644\u0623\u0633\u0627\u0644\u064a\u0628 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u062a\u062d\u064a\u0632\u0629 \u0623\u0646 \u0645\u062b\u0644 \u0647\u0630\u0647 \u0627\u0644\u0623\u0633\u0627\u0644\u064a\u0628 \u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u0648\u0641\u0631 \u062a\u0642\u062f\u064a\u0631\u0627\u062a \u0623\u0641\u0636\u0644 \u0644\u0644\u0645\u0639\u0627\u0644\u0645 \u0628\u0645\u0639\u0646\u0649 \u0627\u0644\u0645\u062a\u0648\u0633\u0637 \u0627\u0644\u0645\u0631\u0628\u0639. \u0648\u0644\u0643\u0646\u0647\u0627 \u0644\u0627 \u062a\u0639\u0646\u064a \u0628\u0627\u0644\u0636\u0631\u0648\u0631\u0629 \u0623\u0646 \u062d\u0644 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u062a\u062d\u064a\u0632 \u0645\u0642\u0628\u0648\u0644 (\u0623\u0648 \u062d\u062a\u0649 \u0623\u0641\u0636\u0644) \u0645\u0646 \u062d\u0644 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 \u0644\u0623\u063a\u0631\u0627\u0636 \u0623\u062e\u0631\u0649 \u063a\u064a\u0631 \u062a\u0642\u062f\u064a\u0631 \u0627\u0644\u0645\u0639\u0627\u0644\u0645. \u0636\u0639 \u0641\u064a \u0627\u0639\u062a\u0628\u0627\u0631\u0643 \u0623\u0646 \u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a \u0644\u0627 \u064a\u0624\u062b\u0631 \u0639\u0644\u0649 \u062f\u0642\u0629 \u0645\u0642\u062f\u0631 \u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0629\u060c \u0641\u0647\u064a \u0644\u0627 \u062a\u0633\u0628\u0628 \u062a\u0636\u062e\u0645 \u0627\u0644\u062a\u0628\u0627\u064a\u0646 \u0641\u064a \u0645\u0642\u062f\u0631\u0627\u062a \u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0629 \u0641\u064a \u0646\u0642\u0627\u0637 \u0623\u062e\u0631\u0649.<\/p>\n<p style=\"text-align: justify;\">\u0623\u0646 \u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0646\u0643\u0645\u0627\u0634 \u0631\u064a\u062f\u062c \u0642\u062f \u062d\u0638\u064a \u0628\u0623\u0643\u0628\u0631 \u0642\u062f\u0631 \u0645\u0646 \u0627\u0644\u0642\u0628\u0648\u0644 \u0644\u062f\u064a \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u0628\u062d\u0627\u062b\u060c \u0648\u0644\u0647\u0630\u0627 \u0641\u0642\u062f \u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647 \u0628\u0646\u062c\u0627\u062d \u0648\u0627\u0636\u062d \u0641\u064a \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u0645\u0634\u0627\u0643\u0644 \u0645\u062e\u062a\u0644\u0641\u0629. \u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0646\u0643\u0645\u0627\u0634 \u0631\u064a\u062f\u062c \u0648\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u0643\u0648\u0646\u0627\u062a \u0627\u0644\u0631\u0626\u064a\u0633\u064a \u0647\u0645\u0627 \u0627\u0644\u0645\u0646\u0627\u0641\u0633\u0627\u0646 \u0627\u0644\u0648\u062d\u064a\u062f\u0627\u0646 \u0645\u0633\u062a\u062e\u062f\u0645\u0627\u0646 \u0641\u064a \u0637\u0631\u0642 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u062a\u062d\u064a\u0632\u0629. \u062a\u0630\u0643\u0631 \u0623\u0646 \u0623\u0633\u0627\u0644\u064a\u0628 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u062a\u062d\u064a\u0632\u0629 \u062a\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a \u0639\u0646 \u0637\u0631\u064a\u0642 \u062a\u0642\u0644\u064a\u0635 \u062a\u0623\u062b\u064a\u0631\u0627\u062a \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u062e\u0637\u064a\u0629 \u0627\u0644\u0645\u062a\u062f\u0627\u062e\u0644\u0629 \u062d\u0633\u0627\u0628\u064a\u064b\u0627.<\/p>\n<p style=\"text-align: justify;\"><strong>2. \u0645\u0642\u062f\u0631\u0627\u062a \u0627\u0644\u0627\u0646\u0643\u0645\u0627\u0634 <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>1.2 \u0645\u0642\u062f\u0645\u0629<\/strong><\/p>\n<p style=\"text-align: justify;\">\u062f\u0639 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u062a\u0648\u0636\u064a\u062d\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645\u0629 \u0641\u064a \u0623\u064a \u062f\u0631\u0627\u0633\u0629 \u0645\u0639\u064a\u0646\u0629 \u064a\u062a\u0645 \u062a\u0631\u062a\u064a\u0628\u0647\u0627 \u0641\u064a \u0634\u0643\u0644 \u0645\u0635\u0641\u0648\u0641\u0629 \u062a\u0633\u0645\u0649 X-matrix. \u064a\u0645\u0643\u0646 \u0635\u064a\u0627\u063a\u0629 \u0627\u0644\u0625\u062c\u0631\u0627\u0621\u0627\u062a \u0627\u0644\u062a\u064a \u0633\u064a\u062a\u0645 \u0639\u0631\u0636\u0647\u0627 \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0628\u062d\u062b \u0643\u0627\u0645\u062a\u062f\u0627\u062f \u0645\u0628\u0627\u0634\u0631 \u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631. \u062a\u062e\u062a\u0644\u0641 \u0647\u0630\u0647 \u0627\u0644\u0625\u062c\u0631\u0627\u0621\u0627\u062a \u0641\u064a \u0645\u0635\u0641\u0648\u0641\u0629 X \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645\u0629 \u0648\u0623\u064a\u0636\u064b\u0627 \u0643\u064a\u0641\u064a\u0629 \u062a\u062d\u062f\u064a\u062f \u062a\u0644\u0643 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629. \u0645\u0647\u0645\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 X \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645\u0629\u060c \u0633\u064a\u0643\u0648\u0646 \u0647\u0646\u0627\u0643 \u0639\u062f\u062f \u0645\u062a\u0633\u0627\u0648 \u0645\u0646 \u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631. \u0643\u0644\u0645\u0627 \u0632\u0627\u062f\u062a \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0645\u0637\u0644\u0642\u0629 \u0644\u0647\u0630\u0647 \u0627\u0644\u0645\u0639\u0627\u0645\u0644\u0627\u062a\u060c \u0643\u0644\u0645\u0627 \u0632\u0627\u062f\u062a \u0627\u062e\u062a\u0644\u0627\u0641 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0645\u0642\u062f\u0631\u0629.<\/p>\n<p style=\"text-align: justify;\">\u0625\u0630\u0627 \u0643\u0627\u0646 \u0645\u0639\u0627\u0645\u0644 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u064a\u0633\u0627\u0648\u064a \u0627\u0644\u0635\u0641\u0631\u060c \u0641\u0633\u062a\u0643\u0648\u0646 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0645\u0642\u062f\u0631\u0629 \u062e\u0637\u064b\u0627 \u0645\u0633\u062a\u0642\u064a\u0645\u064b\u0627 (\u0623\u064a \u0645\u0648\u0627\u0632\u064a\u064b\u0627 \u0644\u0644\u0645\u062d\u0648\u0631 \u0627\u0644\u0633\u064a\u0646\u064a\u060c \u0648\u064a\u062a\u0645 \u0648\u0636\u0639\u0647 \u0639\u0646\u062f \u0627\u0644\u0648\u0633\u0637 \u0627\u0644\u063a\u064a\u0631 \u0645\u0634\u0631\u0648\u0637 \u0644\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0629). \u0645\u0639 \u0632\u064a\u0627\u062f\u0629 \u0645\u0639\u0627\u0645\u0644 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631\u060c \u0633\u062a\u0643\u0648\u0646 \u0644\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0646\u0627\u062a\u062c\u0629 \u0627\u0644\u0645\u062a\u062f\u0631\u062c\u0629 \u0623\u062b\u0631 \u0641\u064a \u0632\u064a\u0627\u062f\u0629 \u0627\u0644\u062d\u062c\u0645. \u064a\u0635\u0628\u062d \u062e\u0637 \u0627\u0644\u062a\u0642\u062f\u064a\u0631 \u0623\u0642\u0644 \u0627\u0646\u062a\u0638\u0627\u0645\u064b\u0627. \u0648\u0628\u0634\u0643\u0644 \u0639\u0627\u0645\u060c \u0641\u0625\u0646 \u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0639\u062f\u0645 \u0627\u0644\u0627\u0646\u062a\u0638\u0627\u0645 \u062a\u0643\u0648\u0646 \u0623\u0643\u0628\u0631 \u0645\u0639 \u0632\u064a\u0627\u062f\u0629 \u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 (Hoerl and Kennard, 1975).<\/p>\n<p style=\"text-align: justify;\">\u062a\u0645 \u062a\u0642\u062f\u064a\u0645 \u0627\u0642\u062a\u0631\u0627\u062d\u064a\u0646 \u0634\u0627\u0626\u0639\u064a\u0646 \u0644\u0643\u064a\u0641\u064a\u0629 \u0627\u0644\u062a\u062d\u0643\u0645 \u0641\u064a \u062d\u062c\u0645 \u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631\u060c \u0648\u0647\u0645\u0627: .<\/p>\n<p style=\"text-align: justify;\">\u062c\u0632\u0627\u0626\u064a\u0629 L<sub>1<\/sub>: \u062a\u0642\u064a\u064a\u062f \u0645\u062c\u0645\u0648\u0639 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0645\u0637\u0644\u0642\u0629 \u0644\u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0644\u064a\u0643\u0648\u0646 \u0623\u0642\u0644 \u0645\u0646 \u0628\u0639\u0636 \u0627\u0644\u062b\u0648\u0627\u0628\u062a C .<\/p>\n<p style=\"text-align: justify;\">\u062c\u0632\u0627\u0626\u064a\u0629 L<sub>2<\/sub>:: \u062a\u0642\u064a\u064a\u062f \u0645\u062c\u0645\u0648\u0639 \u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u0631\u0628\u0639\u0629 \u0644\u064a\u0643\u0648\u0646 \u0623\u0642\u0644 \u0645\u0646 \u0628\u0639\u0636 \u0627\u0644\u062b\u0627\u0628\u062a C.<\/p>\n<p style=\"text-align: justify;\">\u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u0643\u0644\u0645\u0627 \u0643\u0627\u0646\u062a \u0642\u064a\u0645\u0629 C \u0623\u0635\u063a\u0631\u060c \u0643\u0627\u0646 \u0627\u0644\u0645\u062c\u0645\u0648\u0639 \u0623\u0635\u063a\u0631. \u0648\u0643\u0644\u0645\u0627 \u0643\u0627\u0646 \u0627\u0644\u0645\u062c\u0645\u0648\u0639 \u0623\u0635\u063a\u0631\u060c \u0643\u0644\u0645\u0627 \u0643\u0627\u0646\u062a \u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0623\u0635\u063a\u0631 \u0641\u064a \u0627\u0644\u062d\u062c\u0645. \u0648\u0628\u0628\u0633\u0627\u0637\u0629 \u0641\u0623\u0646 \u0647\u0630\u0627\u0646 \u0627\u0644\u0642\u064a\u062f\u0627\u0646 \u064a\u0624\u062f\u064a\u0627\u0646 \u0625\u0644\u0649 \u0645\u0627 \u064a\u0633\u0645\u0649 \u0628\u0637\u0631\u0642 \u0627\u0644\u0627\u0646\u0643\u0645\u0627\u0634\u060c \u0641\u0639\u0646\u062f\u0645\u0627 \u064a\u062a\u0645 \u062a\u0642\u0644\u064a\u0635 \u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0646\u062d\u0648 \u0627\u0644\u0635\u0641\u0631\u060c \u064a\u062c\u0639\u0644 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0645\u0642\u062f\u0631\u0629 \u0623\u0643\u062b\u0631 \u062a\u062c\u0627\u0646\u0633\u064b\u0627. \u0648\u0644\u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0627\u0644\u0647\u062f\u0641 \u0627\u0644\u0631\u0626\u064a\u0633\u064a \u0647\u0648 \u0625\u062f\u062e\u0627\u0644 \u0642\u062f\u0631 \u0635\u063a\u064a\u0631 \u0645\u0646 \u0627\u0644\u062a\u062d\u064a\u0632 \u0641\u064a \u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u062d\u0633\u0648\u0628\u0629 \u0641\u064a \u0627\u062c\u0644 \u0627\u0644\u0645\u0642\u0627\u064a\u0636\u0629 \u0644\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0642\u062f\u0631 \u0643\u0628\u064a\u0631 \u0645\u0646 \u0627\u0644\u062a\u062e\u0641\u064a\u0636 \u0641\u064a \u062a\u0628\u0627\u064a\u0646\u0647\u0627.<\/p>\n<p style=\"text-align: justify;\">\u064a\u062a\u0645 \u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u0627\u0646\u0643\u0645\u0627\u0634 \u0639\u0644\u0649 \u062a\u0642\u062f\u064a\u0631\u0627\u062a \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u0639\u062a\u0627\u062f\u0629 \u0644\u0647\u062f\u0641\u064a\u0646:<\/p>\n<p style=\"text-align: justify;\">\u0623\u0648\u0644\u0627\u060c \u0644\u0644\u0645\u0647\u062a\u0645\u064a\u0646 \u0641\u064a \u0627\u062e\u062a\u064a\u0627\u0631 \u0627\u0644\u0646\u0645\u0648\u0630\u062c. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u064a\u0645\u0643\u0646 \u0644\u0623\u0642\u0644 \u0645\u0634\u063a\u0644 \u0627\u0644\u0627\u0646\u0643\u0645\u0627\u0634 \u0648\u0627\u0644\u0627\u062e\u062a\u064a\u0627\u0631 \u0645\u0637\u0644\u0642\u064b\u0627 (Least Absolute Shrinkage and Selection Operator) <strong>LASSO<\/strong> \u062a\u0648\u0641\u064a\u0631 \u0628\u062f\u0627\u0626\u0644 \u0645\u0641\u064a\u062f\u0629 \u0644\u0625\u062c\u0631\u0627\u0621\u0627\u062a \u0627\u062e\u062a\u064a\u0627\u0631 \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u0627\u0644\u0645\u0639\u062a\u0627\u062f\u0629.<\/p>\n<p style=\"text-align: justify;\">\u062b\u0627\u0646\u064a\u0627\u064b\u060c \u0627\u0644\u0645\u0647\u062a\u0645\u0648\u0646 \u0628\u062a\u062d\u0642\u064a\u0642 \u062a\u0648\u0627\u0632\u0646 \u062c\u064a\u062f \u0628\u064a\u0646 \u0627\u0644\u062a\u062d\u064a\u0632 \u0648\u0627\u0644\u062a\u0628\u0627\u064a\u0646. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u064a\u0645\u0643\u0646 \u0644\u0645\u0642\u062f\u0631 \u0627\u0646\u062d\u062f\u0627\u0631 \u0631\u064a\u062f\u062c (<strong>Ridge<\/strong> ) \u0627\u0644\u0627\u0646\u0643\u0645\u0627\u0634\u064a \u0623\u0646 \u064a\u0648\u0641\u0631 \u0628\u062f\u0627\u0626\u0644 \u0645\u0641\u064a\u062f\u0629 \u0644\u0645\u0639\u0627\u0644\u062c\u0629 \u0645\u0642\u0627\u064a\u0636\u0629 \u0627\u0644\u062a\u062d\u064a\u0632 \u0648\u0627\u0644\u062a\u0628\u0627\u064a\u0646 \u0641\u064a \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u0639\u062a\u0627\u062f (Baltagi, 2001).<\/p>\n<p style=\"text-align: justify;\"><strong>2.2 \u0645\u0642\u062f\u0645\u0629 \u0641\u064a \u0627\u0646\u062d\u062f\u0627\u0631 \u0631\u064a\u062f\u062c (Ridge Regression)<\/strong><\/p>\n<p style=\"text-align: justify;\">\u0628\u0634\u0643\u0644 \u0639\u0627\u0645\u060c \u064a\u0639\u062a\u0628\u0631 \u0627\u0646\u062d\u062f\u0627\u0631 \u0631\u064a\u062f\u062c \u0627\u0644\u0627\u0646\u0643\u0645\u0627\u0634\u064a (\u064cRidge Shrinkage) \u0623\u062d\u062f \u0627\u0644\u062a\u062f\u0627\u0628\u064a\u0631 \u0627\u0644\u0639\u0644\u0627\u062c\u064a\u0629 \u0627\u0644\u0623\u0643\u062b\u0631 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u064b\u0627 \u0644\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a \u0639\u0646\u062f \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062a\u0642\u062f\u064a\u0631 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 \u0627\u0644\u0627\u0639\u062a\u064a\u0627\u062f\u064a\u0629.<\/p>\n<p style=\"text-align: justify;\">\u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a \u062a\u062d\u062f\u062b \u0639\u0646\u062f\u0645\u0627 \u062a\u0643\u0648\u0646 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u062a\u0648\u0636\u064a\u062d\u064a\u0629 \u0627\u0644\u0645\u0636\u0645\u0646\u0629 \u0641\u064a \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u0627\u0644\u062e\u0637\u064a \u0645\u0631\u062a\u0628\u0637\u0629 \u0628\u0634\u0643\u0644 \u0643\u0628\u064a\u0631 \u0645\u0639 \u0628\u0639\u0636\u0647\u0627 \u0627\u0644\u0628\u0639\u0636. \u0639\u0646\u062f\u0645\u0627 \u064a\u062d\u062f\u062b \u0647\u0630\u0627\u060c \u0641\u0625\u0646 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 X<sup>t<\/sup> X \u062a\u0645\u064a\u0644 \u0625\u0644\u0649 \u0625\u0646\u062a\u0627\u062c \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0634\u0627\u0630\u0629. \u0648\u0646\u062a\u064a\u062c\u0629 \u0644\u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u062a\u062d\u062f\u064a\u062f \u062a\u0642\u062f\u064a\u0631\u0627\u062a \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 \u0633\u064a\u0648\u0627\u062c\u0647 \u0628\u0627\u0644\u062a\u0623\u0643\u064a\u062f \u0645\u0634\u0627\u0643\u0644 \u0639\u062f\u062f\u064a\u0629. \u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0646\u0643\u0645\u0627\u0634 \u0631\u064a\u062f\u062c (Ridge Shrinkage) \u0647\u0648 \u0646\u0648\u0639 \u0645\u0642\u064a\u062f \u0645\u0646 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649. \u0625\u0646\u0647 \u064a\u062d\u0644 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0642\u062f\u064a\u0631 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0625\u0646\u062a\u0627\u062c \u0645\u0642\u062f\u0631 \u0645\u062a\u062d\u064a\u0632\u060c \u0645\u0639 \u0648\u062c\u0648\u062f \u062a\u0628\u0627\u064a\u0646\u0627\u062a \u0635\u063a\u064a\u0631\u0629 (Weisberg 2005)<\/p>\n<p style=\"text-align: justify;\"><strong>1.2.2 \u0627\u0644\u062a\u0637\u0648\u064a\u0631 \u0627\u0644\u0646\u0638\u0631\u064a \u0644\u0645\u0642\u062f\u0631 \u0627\u0646\u0643\u0645\u0627\u0634 \u0631\u064a\u062f\u062c<\/strong><\/p>\n<p style=\"text-align: justify;\"><em>\u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0623\u064a \u0645\u0642\u062f\u0631 \u0644\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 b\u060c \u064a\u0645\u0643\u0646 \u0625\u0639\u0627\u062f\u0629 \u0643\u062a\u0627\u0628\u0629 \u0645\u0639\u064a\u0627\u0631 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 \u0643\u062d\u062f \u0623\u062f\u0646\u0649\u060c \u062d\u064a\u062b \u062a\u0645 \u0627\u0644\u0648\u0635\u0648\u0644 \u0625\u0644\u064a\u0647 \u0639\u0646\u062f . \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u062a\u0631\u0628\u064a\u0639\u064a\u0629<\/em> \u0641\u064a b<\/p>\n<p style=\"text-align: justify;\">Q(b) = Q(b) =<\/p>\n<p style=\"text-align: justify;\">= +<\/p>\n<p style=\"text-align: justify;\">= (3)<\/p>\n<p style=\"text-align: justify;\">\u0643\u0646\u062a\u0648\u0631\u0627\u062a \u0643\u0644 \u062b\u0627\u0628\u062a \u0645\u0646 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u062a\u0631\u0628\u064a\u0639\u064a\u0629 \u0647\u064a \u0623\u0634\u0643\u0627\u0644 hyperellipsoids \u062a\u062a\u0645\u0631\u0643\u0632 \u0639\u0646\u062f \u0645\u0642\u062f\u0631 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 \u0627\u0644\u0627\u0639\u062a\u064a\u0627\u062f\u064a . \u0648\u0645\u0646 \u0627\u0644\u0645\u0639\u0642\u0648\u0644 \u0623\u0646 \u0646\u062a\u0648\u0642\u0639 \u0645\u0646 (3) \u0623\u0646\u0647 \u0625\u0630\u0627 \u062a\u062d\u0631\u0643 \u0627\u0644\u0645\u0631\u0621 \u0628\u0639\u064a\u062f\u064b\u0627 \u0639\u0646 Q<sub>min<\/sub>\u060c \u0641\u0625\u0646 \u0627\u0644\u062d\u0631\u0643\u0629 \u062a\u0643\u0648\u0646 \u0641\u064a \u0627\u062a\u062c\u0627\u0647 \u064a\u0642\u0635\u0631 \u0627\u0644\u0637\u0648\u0644 \u0645\u0646 b.<\/p>\n<p style=\"text-align: justify;\">\u0641\u064a \u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0646\u0643\u0645\u0627\u0634 \u0631\u064a\u062f\u062c Ridge Shrinkage Regression\u060c \u064a\u0645\u0643\u0646 \u062a\u062d\u062f\u064a\u062f \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u062d\u0633\u064a\u0646 \u0639\u0644\u0649 \u0627\u0644\u0646\u062d\u0648 \u0627\u0644\u062a\u0627\u0644\u064a<\/p>\n<p style=\"text-align: justify;\">minimizing \u0645\u0639 \u0645\u0631\u0627\u0639\u0627\u0629 = (4)<\/p>\n<p style=\"text-align: justify;\">\u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0628\u0639\u0636 \u0627\u0644\u062b\u0648\u0627\u0628\u062a \u03d5<sub>0<\/sub>. \u064a\u0636\u0645\u0646 \u0627\u0644\u0642\u064a\u062f \u0627\u0644\u0645\u0641\u0631\u0648\u0636 \u0648\u062c\u0648\u062f \u0645\u062c\u0645\u0648\u0639 \u0645\u0646 \u0627\u0644\u0628\u0648\u0627\u0642\u064a \u0635\u063a\u064a\u0631\u0629 \u0628\u0634\u0643\u0644 \u0645\u0639\u0642\u0648\u0644 \u0645\u0646 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a Q(\u03b2) \u0639\u0646\u062f \u0645\u0642\u0627\u0631\u0646\u062a\u0647\u0627 \u0628\u0627\u0644\u062d\u062f \u0627\u0644\u0623\u062f\u0646\u0649 Q<sub>min<\/sub>. \u064a\u0639\u0631\u0636 \u0627\u0644\u0634\u0643\u0644 2 \u0645\u062d\u064a\u0637 \u0627\u0644\u0645\u062c\u0645\u0648\u0639 \u0627\u0644\u0628\u0648\u0627\u0642\u064a \u0644\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0645\u0639 \u0642\u064a\u062f \u0627\u0646\u0643\u0645\u0627\u0634 \u0627\u0644\u0631\u064a\u062f\u062c L<sub>2<\/sub> \u0641\u064a \u0627\u0644\u062d\u0627\u0644\u0629 \u062b\u0646\u0627\u0626\u064a\u0629 \u0627\u0644\u0623\u0628\u0639\u0627\u062f (Kotz, 2004 and Nadarajah)<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" width=\"530\" height=\"319\" class=\"wp-image-13393\" src=\"http:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-2.png\" srcset=\"https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-2.png 530w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-2-300x181.png 300w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-2-18x12.png 18w\" sizes=\"auto, (max-width: 530px) 100vw, 530px\" \/><\/p>\n<p style=\"text-align: justify;\">\u0627\u0644\u0634\u0643\u0644 (2) <em>\u0643\u0646\u062a\u0648\u0631\u0627\u062a \u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0628\u0648\u0627\u0642\u064a \u0648\u0627\u0644\u0642\u064a\u0648\u062f \u0641\u064a \u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0646\u0643\u0645\u0627\u0634 \u0631\u064a\u062f\u062c Ridge Shrinkage<\/em><\/p>\n<p style=\"text-align: justify;\">\u0648\u0645\u0646 \u0648\u062c\u0647\u0629 \u0646\u0638\u0631 \u0645\u0634\u0643\u0644\u0629 \u0644\u0627\u063a\u0631\u0627\u0646\u062c (Lagrangian)\u060c \u0641\u0647\u064a \u062a\u0639\u0627\u062f\u0644 \u0627\u0644\u062a\u0642\u0644\u064a\u0644<\/p>\n<p style=\"text-align: justify;\">(5)<\/p>\n<p style=\"text-align: justify;\">\u062d\u064a\u062b <em>k<\/em> \u0647\u0648 \u0639\u0627\u0645\u0644 \u0627\u0644\u0627\u0646\u062d\u0631\u0627\u0641 \u0627\u0644\u0645\u062e\u062a\u0627\u0631 \u0644\u0627\u0633\u062a\u0641\u0627\u0621 \u0645\u062a\u0637\u0644\u0628\u0627\u062a \u0627\u0644\u0642\u064a\u062f.<\/p>\n<p style=\"text-align: justify;\">\u0648\u0644\u0630\u0644\u0643\u060c \u0642\u0645 \u0628\u0627\u0644\u062a\u0645\u064a\u064a\u0632 \u0628\u064a\u0646 Q* (\u03b2) \u0641\u064a\u0645\u0627 \u064a\u062a\u0639\u0644\u0642 \u0628\u0640 \u03b2<\/p>\n<p style=\"text-align: justify;\">(\u2202() (6)<\/p>\n<p style=\"text-align: justify;\">\u0627\u0644\u0630\u064a \u064a\u0646\u062a\u062c \u0645\u0642\u062f\u0631 \u0627\u0646\u0643\u0645\u0627\u0634 \u0631\u064a\u062f\u062c Ridge Shrinkage \u0639\u0644\u0649 \u0627\u0644\u0646\u062d\u0648 \u0627\u0644\u062a\u0627\u0644\u064a<\/p>\n<p style=\"text-align: justify;\">= (7)<\/p>\n<p style=\"text-align: justify;\">\u0647\u0646\u0627\u0643 \u0637\u0631\u064a\u0642\u0629 \u0628\u062f\u064a\u0644\u0629 \u062a\u062a\u0645\u062b\u0644 \u0641\u064a \u062a\u0648\u0636\u064a\u062d \u0645\u0634\u0643\u0644\u0629 \u0627\u0646\u0643\u0645\u0627\u0634 \u0631\u064a\u062f\u062c Ridge Shrinkage \u0641\u064a \u0634\u0643\u0644 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 \u0627\u0644\u0645\u0642\u064a\u062f\u0629 \u0628\u0648\u0627\u0633\u0637\u0629<\/p>\n<p style=\"text-align: justify;\">minimizing<\/p>\n<p style=\"text-align: justify;\">\u0644\u0628\u0639\u0636 \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u062b\u0627\u0628\u062a\u0629 \u0644\u0640 s.<\/p>\n<p style=\"text-align: justify;\">\u0648\u0645\u0646 \u0647\u0646\u0627 \u062a\u0635\u0628\u062d \u0645\u0634\u0643\u0644\u0629 \u0644\u0627\u063a\u0631\u0627\u0646\u062c (Lagrangian) \u0645\u062c\u0631\u062f \u0627\u0644\u062a\u0642\u0644\u064a\u0644 \u0645\u0646 \u0630\u0644\u0643<\/p>\n<p style=\"text-align: justify;\">\u0627\u0644\u0630\u064a \u064a\u0646\u062a\u062c \u0646\u0641\u0633 \u0627\u0644\u0645\u0642\u062f\u0631 \u0627\u0644\u0648\u0627\u0631\u062f \u0641\u064a (7) \u062a\u062a\u062d\u0643\u0645 \u0645\u0639\u0644\u0645\u0629 \u0627\u0644\u0639\u0642\u0648\u0628\u0629 \u03bb \u2265 0 \u0641\u064a \u0645\u0642\u062f\u0627\u0631 \u0627\u0644\u0627\u0646\u0643\u0645\u0627\u0634 \u0641\u064a . \u0643\u0644\u0645\u0627 \u0632\u0627\u062f\u062a \u0642\u064a\u0645\u0629 \u03bb \u0643\u0644\u0645\u0627 \u0632\u0627\u062f \u0645\u0642\u062f\u0627\u0631 \u0627\u0644\u0627\u0646\u0643\u0645\u0627\u0634. \u0644\u0647\u0630\u0627 \u0627\u0644\u0633\u0628\u0628\u060c \u0641\u0625\u0646 \u0645\u0642\u062f\u0631 \u0627\u0646\u0643\u0645\u0627\u0634 \u0631\u064a\u062f\u062c \u064a\u0633\u0645\u0649 \u0641\u064a \u0643\u062b\u064a\u0631 \u0645\u0646 \u0627\u0644\u0623\u062d\u064a\u0627\u0646 \u0645\u0642\u062f\u0631 \u0627\u0644\u0627\u0646\u0643\u0645\u0627\u0634 (Bates and Watts, 1988).<\/p>\n<p style=\"text-align: justify;\"><strong><em>3.2 <\/em><\/strong>\u00a0<strong>\u0644\u0627\u0633\u0648 <em>LASSO<\/em><\/strong><em>:<\/em>\u00a0<strong>\u0623\u0642\u0644 \u0639\u0627\u0645\u0644 \u0627\u0646\u0643\u0645\u0627\u0634 \u0648\u0627\u062e\u062a\u064a\u0627\u0631 \u0645\u0637\u0644\u0642<\/strong>\u00a0<\/p>\n<p style=\"text-align: justify;\">(<strong>least absolute shrinkage and selection operator<\/strong>)<strong> LASSO <\/strong><\/p>\n<p style=\"text-align: justify;\"><em>\u064a\u0639\u062a\u0628\u0631 \u0639\u0627\u0645\u0644 \u0627\u0644\u0627\u0646\u0643\u0645\u0627\u0634 \u0648\u0627\u0644\u0627\u062e\u062a\u064a\u0627\u0631 \u0627\u0644\u0623\u0642\u0644 \u0627\u0644\u0645\u0637\u0644\u0642 (<\/em><strong><em>LASSO<\/em><\/strong><em>) \u0637\u0631\u064a\u0642\u0629 \u0627\u0646\u0643\u0645\u0627\u0634 \u0623\u062e\u0631\u0649 \u0645\u062b\u0644 \u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0646\u0643\u0645\u0627\u0634 \u0631\u064a\u062f\u062c\u060c \u0648\u0644\u0643\u0646 \u0645\u0639 \u0645\u064a\u0632\u0629 \u0645\u0647\u0645\u0629 \u0648\u062c\u0630\u0627\u0628\u0629 \u0641\u064a \u0627\u0644\u0627\u062e\u062a\u064a\u0627\u0631 \u0627\u0644\u0645\u062a\u063a\u064a\u0631. \u0628\u062f\u0644\u0627\u064b \u0645\u0646 \u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0646\u0643\u0645\u0627\u0634 \u0631\u064a\u062f\u062c \u064a\u062c\u0639\u0644 \u0639\u0645\u0644\u064a\u0629 \u0627\u0644\u0627\u062e\u062a\u064a\u0627\u0631 \u0645\u0633\u062a\u0645\u0631\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u062a\u063a\u064a\u064a\u0631 \u0645\u0639\u0644\u0645\u0629 \u0627\u0644\u0627\u0646\u0643\u0645\u0627\u0634 k \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u062a\u0635\u0628\u062d \u0623\u0643\u062b\u0631 \u0627\u0633\u062a\u0642\u0631\u0627\u0631\u064b\u0627. \u0645\u0646 \u062e\u0644\u0627\u0644 \u0647\u0630\u0647 \u0627\u0644\u0639\u0645\u0644\u064a\u0629\u060c \u0644\u0627 \u064a\u0636\u0639 \u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0646\u0643\u0645\u0627\u0634 \u0631\u064a\u062f\u062c \u0623\u064a \u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0639\u0644\u0649 \u0627\u0644\u0635\u0641\u0631\u060c \u0644\u0623\u0646\u0647 \u0644\u0627 \u064a\u0639\u0637\u064a \u0646\u0645\u0648\u0630\u062c\u064b\u0627 \u064a\u0645\u0643\u0646 \u062a\u0641\u0633\u064a\u0631\u0647 \u0628\u0633\u0647\u0648\u0644\u0629 \u0643\u0645\u0627 \u0647\u0648 \u0627\u0644\u062d\u0627\u0644 \u0641\u064a \u0627\u062e\u062a\u064a\u0627\u0631 \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0627\u0644\u0641\u0631\u0639\u064a\u0629subset selection ( Greene, 2000).<\/em><\/p>\n<p style=\"text-align: justify;\"><em>\u062a\u0645 \u0627\u0642\u062a\u0631\u0627\u062d \u062a\u0643\u062a\u064a\u0643 <\/em><strong><em>LASSO<\/em><\/strong><em> \u0644\u0644\u062d\u0641\u0627\u0638 \u0639\u0644\u0649 \u0645\u0632\u0627\u064a\u0627 \u0627\u062e\u062a\u064a\u0627\u0631 \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0627\u0644\u0641\u0631\u0639\u064a\u0629 \u0648\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0646\u0643\u0645\u0627\u0634 \u0631\u064a\u062f\u062c \u0639\u0646 \u0637\u0631\u064a\u0642 \u062a\u0642\u0644\u064a\u0635 \u0628\u0639\u0636 \u0627\u0644\u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0646\u0645\u0648\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0648\u0636\u0628\u0637 \u0627\u0644\u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0646\u0645\u0648\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0623\u062e\u0631\u0649 \u0639\u0644\u0649 \u0627\u0644\u0635\u0641\u0631. \u064a\u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0645\u0642\u062f\u0631 <\/em><strong><em>LASSO<\/em><\/strong> <em>\u0644\u0640 \u03b2 \u0628\u0648\u0627\u0633\u0637\u0629 <\/em><\/p>\n<p style=\"text-align: justify;\"><em>minimizing ..<\/em><\/p>\n<p style=\"text-align: justify;\"><em>\u0648\u0628\u0634\u0643\u0644 \u0623\u0643\u062b\u0631 \u0648\u0636\u0648\u062d\u064b\u0627\u060c \u064a\u062a\u0645 \u0627\u0633\u062a\u0628\u062f\u0627\u0644 (L<sub>2<\/sub> \u0628\u062c\u0632\u0627\u0621 ) \u0641\u064a \u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0646\u0643\u0645\u0627\u0634 \u0631\u064a\u062f\u062c \u0628\u0640 L<sub>1<\/sub> \u0628\u062c\u0632\u0627\u0621 \u0641\u064a <\/em><strong><em>LASSO<\/em><\/strong>.<em> \u0625\u0630\u0627 \u062a\u0645 \u0627\u062e\u062a\u064a\u0627\u0631 s \u0644\u062a\u0643\u0648\u0646 \u0623\u0643\u0628\u0631 \u0645\u0646 \u0623\u0648 \u062a\u0633\u0627\u0648\u064a \u060c \u0641\u0625\u0646 \u062a\u0642\u062f\u064a\u0631\u0627\u062a <\/em><strong><em>LASSO<\/em><\/strong><em> \u0647\u064a \u062a\u0645\u0627\u0645\u064b\u0627 \u0646\u0641\u0633 \u062a\u0642\u062f\u064a\u0631 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649. \u0625\u0630\u0627 \u062a\u0645 \u0627\u062e\u062a\u064a\u0627\u0631 s \u0644\u062a\u0643\u0648\u0646 \u0623\u0635\u063a\u0631 \u0645\u0646\u060c \u0641\u0633\u0648\u0641 \u064a\u062a\u0633\u0628\u0628 \u0630\u0644\u0643 \u0641\u064a \u0627\u0646\u0643\u0645\u0627\u0634 \u0627\u0644\u062d\u0644\u0648\u0644 \u0646\u062d\u0648 \u0627\u0644\u0635\u0641\u0631.<\/em><\/p>\n<p style=\"text-align: justify;\">\u064a\u0639\u0631\u0636 \u0627\u0644\u0634\u0643\u0644 3 \u0643\u0646\u062a\u0648\u0631\u0627\u062a \u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0628\u0648\u0627\u0642\u064a \u0645\u0639 \u0642\u064a\u062f L<sub>1<\/sub> <strong>LASSO<\/strong> \u0641\u064a \u0627\u0644\u062d\u0627\u0644\u0629 \u062b\u0646\u0627\u0626\u064a\u0629 \u0627\u0644\u0623\u0628\u0639\u0627\u062f (Greene, 2000)<\/p>\n<p style=\"text-align: justify;\">\u0627\u0644\u0634\u0643\u0644 (3) <em> \u0643\u0646\u062a\u0648\u0631\u0627\u062a \u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0628\u0648\u0627\u0642\u064a \u0648\u062f\u0648\u0627\u0644 \u0627\u0644\u0642\u064a\u0648\u062f \u0641\u064a <\/em><strong>LASSO<\/strong><em>.<\/em><\/p>\n<p style=\"text-align: justify;\"><em>\u062a\u062c\u062f\u0631 \u0627\u0644\u0625\u0634\u0627\u0631\u0629 \u0625\u0644\u0649 \u0623\u0646\u0647 \u0641\u064a \u0627\u0644\u0634\u0643\u0644 <\/em>2<em>\u060c \u0645\u0646\u0637\u0642\u0629 \u0627\u0644\u0642\u064a\u062f \u0641\u064a \u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0646\u0643\u0645\u0627\u0634 \u0631\u064a\u062f\u062c <\/em>Ridge Shrinkage Regression <em> \u0644\u0647\u0627 \u0634\u0643\u0644 \u0642\u0631\u0635. \u0628\u064a\u0646\u0645\u0627 \u0641\u064a \u0627\u0644\u0634\u0643\u0644 <\/em>3<em>\u060c \u0645\u0646\u0637\u0642\u0629 \u0627\u0644\u0642\u064a\u062f \u0641\u064a <\/em><strong><em>LASSO<\/em><\/strong><em> \u0644\u0647\u0627 \u0634\u0643\u0644 \u0645\u0627\u0633\u064a. \u064a\u0645\u0643\u0646 \u0645\u0644\u0627\u062d\u0638\u0629 \u0623\u0646 \u0643\u0644\u0627\u064b \u0645\u0646 \u0637\u0631\u064a\u0642\u062a\u064a \u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0646\u0643\u0645\u0627\u0634 \u0631\u064a\u062f\u062c <\/em>Ridge Shrinkage Regression <em>\u0648 <\/em><strong><em>LASSO<\/em><\/strong><em> \u062a\u0628\u062f\u0623 \u0628\u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0623\u0648\u0644\u0649 \u0627\u0644\u062a\u064a \u062a\u0635\u0637\u062f\u0645 \u0641\u064a\u0647\u0627 \u0627\u0644\u062e\u0637\u0648\u0637 \u0627\u0644\u0628\u064a\u0636\u0627\u0648\u064a\u0629 \u0628\u0645\u0646\u0637\u0642\u0629 \u0627\u0644\u0642\u064a\u062f. \u0648\u0644\u0643\u0646\u060c \u0639\u0644\u0649 \u0639\u0643\u0633 \u062d\u0627\u0644\u0629 \u0627\u0644\u0642\u0631\u0635 <\/em>Ridge Shrinkage Regression<em>\u060c \u0641\u0625\u0646 \u0627\u0644\u0645\u0627\u0633\u0629 \u0627\u0644\u0645\u0648\u062c\u0648\u062f\u0629 \u0641\u064a <\/em><strong><em>LASSO<\/em><\/strong><em> \u0628\u0647\u0627 \u0632\u0648\u0627\u064a\u0627. \u0625\u0630\u0627 \u062d\u062f\u062b \u0627\u0644\u062d\u0644 \u0639\u0646\u062f \u0632\u0627\u0648\u064a\u0629\u060c \u0641\u0625\u0646 \u0645\u0639\u0627\u0645\u0644\u0647 \u064a\u0633\u0627\u0648\u064a \u0627\u0644\u0635\u0641\u0631. \u0648\u064a\u0645\u0643\u0646 \u0623\u064a\u0636\u064b\u0627 \u0645\u0644\u0627\u062d\u0638\u0629 \u0623\u0646 \u062d\u0644<\/em> <strong><em>LASSO<\/em><\/strong><em> \u064a\u062a\u0646\u0627\u0641\u0633 \u0645\u0639 \u062d\u0644 \u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0646\u0643\u0645\u0627\u0634 <\/em>\u0631\u064a\u062f\u062cRidge Shrinkage Regression<em> \u0648\u0644\u0643\u0646 \u0645\u0639 \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u062a\u0642\u062f\u064a\u0631\u0627\u062a \u0627\u0644\u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0646\u0645\u0648\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0635\u0641\u0631\u064a\u0629. \u0641\u064a \u062d\u0627\u0644\u0629 \u0627\u0644\u062a\u0635\u0645\u064a\u0645\u0627\u062a \u0627\u0644\u0645\u062a\u0639\u0627\u0645\u062f\u0629 \u062d\u064a\u062b = I\u060c \u064a\u0645\u0643\u0646 \u0643\u062a\u0627\u0628\u0629 \u0645\u0642\u062f\u0631<\/em><strong> <em>LASSO<\/em><\/strong><em> \u0643\u0640<\/em><\/p>\n<p style=\"text-align: justify;\">= sign<sub>+<\/sub> (8)<\/p>\n<p style=\"text-align: justify;\"><em>\u062d\u064a\u062b \u064a\u062a\u0645 \u062a\u062d\u062f\u064a\u062f \u03b3 \u0628\u0648\u0627\u0633\u0637\u0629 \u0627\u0644\u0634\u0631\u0637 <\/em><\/p>\n<p style=\"text-align: justify;\"><em>\u0644\u0642\u062f \u0642\u0627\u0631\u0646\u0627 \u0623\u062f\u0627\u0621 \u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0646\u0643\u0645\u0627\u0634 \u0631\u064a\u062f\u062c Ridge Shrinkage Regression \u0648 <\/em><strong><em>LASSO<\/em><\/strong> <em>\u0641\u064a \u0633\u064a\u0627\u0642 \u0623\u0643\u0628\u0631. \u0627\u0644\u0627\u0647\u062a\u0645\u0627\u0645 \u0627\u0644\u0631\u0626\u064a\u0633\u064a \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0628\u062d\u062b \u0647\u0648 \u0623\u0646\u0645\u0627\u0637 \u0627\u0644\u0627\u0646\u0643\u0645\u0627\u0634 \u0645\u0639 \u062a\u063a\u064a\u0631 \u03bb. \u064a\u0645\u064a\u0644 \u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0646\u0643\u0645\u0627\u0634 \u0631\u064a\u062f\u062c \u0625\u0644\u0649 \u062a\u0642\u0644\u064a\u0635 \u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0646\u0645\u0648\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0628\u062d\u064a\u062b \u062a\u0635\u0644 \u062c\u0645\u064a\u0639\u0647\u0627 \u0625\u0644\u0649 \u0627\u0644\u0635\u0641\u0631 \u0645\u0639\u064b\u0627 \u0639\u0646\u062f\u0645\u0627 \u062a\u0635\u0628\u062d \u03bb \u0643\u0628\u064a\u0631\u0629. \u064a\u0642\u0648\u0645 <\/em><strong><em>LASSO<\/em><\/strong><em> \u0628\u062a\u0642\u0644\u064a\u0635 \u0627\u0644\u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0628\u062d\u064a\u062b \u064a\u0635\u0644 \u0628\u0639\u0636\u0647\u0627 \u0625\u0644\u0649 \u0627\u0644\u0635\u0641\u0631 \u0642\u0628\u0644 \u0627\u0644\u0628\u0639\u0636 \u0627\u0644\u0622\u062e\u0631 \u0639\u0646\u062f\u0645\u0627 \u062a\u0635\u0628\u062d \u03bb \u0643\u0628\u064a\u0631\u0629 (Hastie et al., 2002).<\/em><\/p>\n<p style=\"text-align: justify;\"><strong>4.2 \u0645\u0642\u062f\u0631 LASSO \u0627\u0644\u062a\u0643\u064a\u0641\u064a<\/strong><\/p>\n<p style=\"text-align: justify;\">\u062f\u0639\u0648\u0646\u0627 \u0646\u0641\u0643\u0631 \u0641\u064a \u0627\u0646\u062d\u062f\u0627\u0631 LASSO \u0627\u0644\u0645\u0631\u062c\u062d<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" width=\"333\" height=\"67\" class=\"wp-image-13394\" src=\"http:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-4.png\" srcset=\"https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-4.png 333w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-4-300x60.png 300w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-4-18x4.png 18w\" sizes=\"auto, (max-width: 333px) 100vw, 333px\" \/> (9)<\/p>\n<p style=\"text-align: justify;\">\u062d\u064a\u062b wj \u0647\u0648 \u0646\u0627\u0642\u0644 \u0623\u0648\u0632\u0627\u0646 \u0645\u0639\u0631\u0648\u0641. \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u0623\u0648\u0632\u0627\u0646 \u062a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0648\u062a\u0645 \u0627\u062e\u062a\u064a\u0627\u0631\u0647\u0627 \u0628\u0639\u0646\u0627\u064a\u0629\u060c \u0641\u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u062d\u062a\u0648\u064a LASSO \u0627\u0644\u0645\u0648\u0632\u0648\u0646\u0629 \u0639\u0644\u0649 \u062e\u0635\u0627\u0626\u0635 Oracle.<\/p>\n<p style=\"text-align: justify;\">\u062a\u0633\u0645\u0649 \u0627\u0644\u0645\u0646\u0647\u062c\u064a\u0629 \u0627\u0644\u062c\u062f\u064a\u062f\u0629 \u0627\u0646\u062d\u062f\u0627\u0631 LASSO \u0627\u0644\u062a\u0643\u064a\u0641\u064a (ALASSO).<\/p>\n<p style=\"text-align: justify;\"><strong>1.4.2 \u062a\u0639\u0631\u064a\u0641 \u0627\u0646\u062d\u062f\u0627\u0631 LASSO \u0627\u0644\u062a\u0643\u064a\u0641\u064a<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong><sup>\u02c4<\/sup><\/strong><\/p>\n<p style=\"text-align: justify;\">\u0644\u0646\u0641\u062a\u0631\u0636 \u0623\u0646 \u03b2 \u0647\u0648 \u0645\u0642\u062f\u0631 \u0627\u0644\u062c\u0630\u0631 n \u0627\u0644\u0645\u062a\u0633\u0642 \u0644\u0640 \u03b2\u061b \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u03b2 (\u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 OLS). \u0627\u062e\u062a\u0631 <img loading=\"lazy\" decoding=\"async\" width=\"44\" height=\"22\" class=\"wp-image-13395\" src=\"http:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-5.png\" srcset=\"https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-5.png 44w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-5-18x9.png 18w\" sizes=\"auto, (max-width: 44px) 100vw, 44px\" \/> \u060c \u0648\u062d\u062f\u062f \u0645\u062a\u062c\u0647 \u0627\u0644\u0648\u0632\u0646 w<sub>j\\<\/sub>=1\/ |\u03b2<sub>j<\/sub>|.<\/p>\n<p style=\"text-align: justify;\">\u064a\u062a\u0645 \u0625\u0639\u0637\u0627\u0621 Adaptive LASSO \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645 \u0644\u062a\u0642\u062f\u064a\u0631 \u03b2 \u0628\u0648\u0627\u0633\u0637\u0629<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" width=\"296\" height=\"62\" class=\"wp-image-13396\" src=\"http:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-6.png\" srcset=\"https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-6.png 296w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-6-18x4.png 18w\" sizes=\"auto, (max-width: 296px) 100vw, 296px\" \/> (10)<\/p>\n<p style=\"text-align: justify;\">\u0648\u0628\u0627\u0644\u0645\u062b\u0644\u060c \u062f\u0639 <em>j<\/em>: where <em>\u03b2<\/em><sub>j<\/sub><sup>n <\/sup> A<sub>n<\/sub> [\u062a\u062c\u062f\u0631 \u0627\u0644\u0625\u0634\u0627\u0631\u0629 \u0625\u0644\u0649 \u0623\u0646 \u03b2<sup>*n<\/sup> \u0647\u064a \u0645\u0634\u0643\u0644\u0629 \u062a\u062d\u0633\u064a\u0646 \u0645\u062d\u062f\u0628\u0629\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0647\u064a \u0644\u0627 \u062a\u0639\u0627\u0646\u064a \u0645\u0646 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u062f\u0646\u0649 \u0627\u0644\u0645\u062d\u0644\u064a \u0627\u0644\u0645\u062a\u0639\u062f\u062f\u0629\u060c \u0648\u064a\u0645\u0643\u0646 \u062d\u0644 \u0623\u062f\u0627\u0629 \u0627\u0644\u062a\u0635\u063a\u064a\u0631 \u0627\u0644\u0639\u0627\u0644\u0645\u064a\u0629 \u0627\u0644\u062e\u0627\u0635\u0629 \u0628\u0647\u0627 \u0628\u0643\u0641\u0627\u0621\u0629 (\u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" width=\"383\" height=\"74\" class=\"wp-image-13397\" src=\"http:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-7.png\" srcset=\"https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-7.png 383w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-7-300x58.png 300w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-7-18x3.png 18w\" sizes=\"auto, (max-width: 383px) 100vw, 383px\" \/><\/p>\n<p style=\"text-align: justify;\">\u0648\u0647\u0630\u0627 \u064a\u062e\u062a\u0644\u0641 \u062a\u0645\u0627\u0645\u064b\u0627 \u0639\u0646 \u0639\u0642\u0648\u0628\u0627\u062a \u0623\u0648\u0631\u0627\u0643\u0644 \u0627\u0644\u0645\u0642\u0639\u0631\u0629. \u064a\u0639\u062f Adaptive LASSO \u0641\u064a \u0627\u0644\u0623\u0633\u0627\u0633 \u0637\u0631\u064a\u0642\u0629 \u0645\u0639\u0627\u0642\u0628\u0629 \u0627\u0644\u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0623\u0648\u0644. \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0641\u0639\u0627\u0644\u0629 \u0627\u0644\u062d\u0627\u0644\u064a\u0629 \u0644\u062d\u0644 LASSO \u0644\u062d\u0633\u0627\u0628 \u062a\u0642\u062f\u064a\u0631\u0627\u062a LASSO \u0627\u0644\u062a\u0643\u064a\u0641\u064a\u0629.<\/p>\n<p style=\"text-align: justify;\">Zou (2006) \u0641\u064a \u0648\u0631\u0642\u062a\u0647 \u0627\u0644\u0645\u0647\u0645\u0629 \u0628\u0639\u0646\u0648\u0627\u0646 &#8220;The Adaptive Lasso \u0648\u062e\u0635\u0627\u0626\u0635 \u0623\u0648\u0631\u0627\u0643\u0644 \u0627\u0644\u062e\u0627\u0635\u0629 \u0628\u0647\u0627&#8221;. \u062a\u0628\u064a\u0646 \u0623\u0646\u0647 \u0645\u0639 \u0627\u0644\u0627\u062e\u062a\u064a\u0627\u0631 \u0627\u0644\u0635\u062d\u064a\u062d \u0644\u060c <img loading=\"lazy\" decoding=\"async\" width=\"10\" height=\"22\" class=\"wp-image-13398\" src=\"http:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-8.png\" srcset=\"https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-8.png 10w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-8-5x12.png 5w\" sizes=\"auto, (max-width: 10px) 100vw, 10px\" \/><sub>\u0646<\/sub>\u064a\u062a\u0645\u062a\u0639 Adaptive LASSO \u0628\u0627\u0644\u062a\u0623\u0643\u064a\u062f \u0628\u062e\u0635\u0627\u0626\u0635 Oracle.<\/p>\n<p style=\"text-align: justify;\"><strong>5.2 \u0645\u0642\u062f\u0631 \u0627\u0644\u0634\u0628\u0643\u0629 \u0627\u0644\u0645\u0631\u0646\u0629 Elastic Net Estimator<\/strong><\/p>\n<p style=\"text-align: justify;\">\u064a\u0639\u062f \u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0634\u0628\u0643\u0629 \u0627\u0644\u0645\u0631\u0646\u0629 <strong>Elastic Net<\/strong>(ENET) \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0642\u0648\u064a\u0629 \u0644\u0644\u062a\u0639\u0644\u0645 \u0627\u0644\u0622\u0644\u064a \u062a\u062c\u0645\u0639 \u0628\u064a\u0646 \u0645\u064a\u0632\u0627\u062a \u0643\u0644 \u0645\u0646 LASSO \u0648Ridge Regression. \u0625\u0646\u0647\u0627 \u062a\u0642\u0646\u064a\u0629 \u0627\u0646\u062d\u062f\u0627\u0631 \u0645\u0646\u062a\u0638\u0645\u0629 \u062a\u064f\u0633\u062a\u062e\u062f\u0645 \u0644\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0645\u0634\u0643\u0644\u0627\u062a \u0627\u0644\u062e\u0637\u064a\u0629 \u0627\u0644\u0645\u062a\u0639\u062f\u062f\u0629 \u0648\u0627\u0644\u0645\u0644\u0627\u0621\u0645\u0629 \u0627\u0644\u0632\u0627\u0626\u062f\u0629\u060c \u0648\u0627\u0644\u062a\u064a \u062a\u0639\u062a\u0628\u0631 \u0634\u0627\u0626\u0639\u0629 \u0641\u064a \u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0639\u0627\u0644\u064a\u0629 \u0627\u0644\u0623\u0628\u0639\u0627\u062f. \u062a\u0639\u0645\u0644 \u0647\u0630\u0647 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0639\u0646 \u0637\u0631\u064a\u0642 \u0625\u0636\u0627\u0641\u0629 \u0645\u0635\u0637\u0644\u062d \u0639\u0642\u0648\u0628\u0629 \u0625\u0644\u0649 \u0627\u0644\u0645\u0639\u064a\u0627\u0631. \u0648\u0638\u064a\u0641\u0629 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 \u0627\u0644\u0647\u062f\u0641. \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0642\u0633\u0645 \u0627\u0644\u0641\u0631\u0639\u064a \u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0633\u0646\u0642\u062f\u0645 \u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0634\u0628\u0643\u0629 \u0627\u0644\u0645\u0631\u0646\u0629 (ENET) \u0628\u0645\u0632\u064a\u062f \u0645\u0646 \u0627\u0644\u062a\u0641\u0627\u0635\u064a\u0644\u060c \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0645\u0632\u0627\u064a\u0627\u0647 \u0648\u0639\u064a\u0648\u0628\u0647.<\/p>\n<p style=\"text-align: justify;\"><strong>1.5.2 \u0646\u0638\u0631\u0629 \u0639\u0627\u0645\u0629 \u0639\u0644\u0649 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0635\u0627\u0641\u064a \u0627\u0644\u0645\u0631\u0646<\/strong><\/p>\n<p style=\"text-align: justify;\">\u062a\u0645 \u062a\u0642\u062f\u064a\u0645 \u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0634\u0628\u0643\u0629 \u0627\u0644\u0645\u0631\u0646\u0629 (ENET) \u0628\u0648\u0627\u0633\u0637\u0629 ( Zou and Hastie )2005 \u0625\u0646\u0647\u0627 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0646\u062d\u062f\u0627\u0631 \u062e\u0637\u064a \u062a\u0636\u064a\u0641 \u0634\u0631\u0637\u064a\u0646 \u062c\u0632\u0627\u0626\u064a\u064a\u0646 \u0625\u0644\u0649 \u062f\u0627\u0644\u0629 \u0627\u0644\u0647\u062f\u0641 \u0627\u0644\u0642\u064a\u0627\u0633\u064a\u0629 \u0630\u0627\u062a \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649. \u0647\u0630\u064a\u0646 \u0627\u0644\u062d\u062f\u064a\u0646 \u0627\u0644\u062c\u0632\u0627\u0626\u064a\u064a\u0646 \u0647\u0645\u0627 \u0645\u0639\u0627\u064a\u064a\u0631 L1 \u0648L2 \u0644\u0645\u062a\u062c\u0647 \u0627\u0644\u0645\u0639\u0627\u0645\u0644\u060c \u0648\u0627\u0644\u062a\u064a \u064a\u062a\u0645 \u0636\u0631\u0628\u0647\u0627 \u0628\u0645\u0639\u0644\u0645\u062a\u064a\u0646 \u0645\u0641\u0631\u0637\u062a\u064a\u0646 \u03b3 \u0648 \u03bb. \u064a\u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0639\u064a\u0627\u0631 L1 \u0644\u0623\u062f\u0627\u0621 \u0645\u064a\u0632\u0629 \u0627\u0644\u0627\u062e\u062a\u064a\u0627\u0631\u060c \u0641\u064a \u062d\u064a\u0646 \u064a\u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0639\u064a\u0627\u0631 L2 \u0644\u0623\u062f\u0627\u0621 \u0645\u064a\u0632\u0629 \u0627\u0644\u062a\u062e\u0641\u064a\u0636.<\/p>\n<p style=\"text-align: justify;\">\u064a\u0645\u0643\u0646 \u062a\u0645\u062b\u064a\u0644 \u0646\u0645\u0648\u0630\u062c \u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0634\u0628\u0643\u0629 \u0627\u0644\u0645\u0631\u0646\u0629 (ENET) \u0639\u0644\u0649 \u0627\u0644\u0646\u062d\u0648 \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p style=\"text-align: justify;\">y = b<sub>0 <\/sub>+ b<sub>1<\/sub> x<sub>1 <\/sub>+ b<sub>2 <\/sub> x<sub>2<\/sub>+\u2026\u2026\u2026. + b<sub>n<\/sub> x<sub>n <\/sub>+ \u03b5<\/p>\n<p style=\"text-align: justify;\">\u062d\u064a\u062b y \u0647\u0648 \u0627\u0644\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u062a\u0627\u0628\u0639\u060c b<sub>0<\/sub> \u0648\u0647\u0648 \u0627\u0644\u062a\u0642\u0627\u0637\u0639\u060c \u0648b<sub>1<\/sub>\u060c\u2026.,b<sub>n<\/sub> \u0647\u064a \u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631\u060c \u0648x<sub>1<\/sub>\u060c\u2026.,x<sub>n<\/sub> \u0647\u064a \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0642\u0644\u0629\u060c \u0648\u03b5 \u0647\u0648 \u0645\u0635\u0637\u0644\u062d \u0627\u0644\u062e\u0637\u0623. \u064a\u062d\u0627\u0648\u0644 \u0646\u0645\u0648\u0630\u062c \u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0634\u0628\u0643\u0629 \u0627\u0644\u0645\u0631\u0646\u0629 (ENET) \u062a\u0642\u0644\u064a\u0644 \u0627\u0644\u0648\u0638\u064a\u0641\u0629 \u0627\u0644\u0647\u062f\u0641 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p style=\"text-align: justify;\">[ RSS + ]( 1-<sup>2 <\/sup>+ a <sup>1<\/sup>[<\/p>\n<p style=\"text-align: justify;\">\u062d\u064a\u062b RSS \u0647\u0648 \u0645\u062c\u0645\u0648\u0639 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0645\u062a\u0628\u0642\u064a\u0629\u060c \u0648\u0645\u0639\u0644\u0645\u0629 \u0627\u0644\u062a\u0646\u0638\u064a\u0645\u060c <img loading=\"lazy\" decoding=\"async\" width=\"12\" height=\"22\" class=\"wp-image-13400\" src=\"http:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-9.png\" srcset=\"https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-9.png 12w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-9-7x12.png 7w\" sizes=\"auto, (max-width: 12px) 100vw, 12px\" \/> \u060c \u0647\u0648 \u0646\u0627\u0642\u0644 \u0627\u0644\u0645\u0639\u0627\u0645\u0644\u060c \u0648\u0647\u0648 \u0645\u0639\u0644\u0645\u0629 \u0627\u0644\u062e\u0644\u0637 \u0628\u064a\u0646 L\u2081 \u0648L\u2082\u060c \u0648\u0627\u0644\u0642\u0648\u0627\u0639\u062f\u060c<sup>2<\/sup> <img loading=\"lazy\" decoding=\"async\" width=\"44\" height=\"22\" class=\"wp-image-13401\" src=\"http:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-10.png\" srcset=\"https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-10.png 44w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-10-18x9.png 18w\" sizes=\"auto, (max-width: 44px) 100vw, 44px\" \/> \u0647\u0648 \u0627\u0644\u0645\u0639\u064a\u0627\u0631 L\u2082 \u0644\u0640 <img loading=\"lazy\" decoding=\"async\" width=\"12\" height=\"22\" class=\"wp-image-13402\" src=\"http:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-11.png\" srcset=\"https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-11.png 12w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-11-7x12.png 7w\" sizes=\"auto, (max-width: 12px) 100vw, 12px\" \/> \u0648<sup>1<\/sup> <img loading=\"lazy\" decoding=\"async\" width=\"40\" height=\"22\" class=\"wp-image-13403\" src=\"http:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-12.png\" srcset=\"https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-12.png 40w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-12-18x10.png 18w\" sizes=\"auto, (max-width: 40px) 100vw, 40px\" \/> \u0647\u0648 \u0645\u0639\u064a\u0627\u0631 L\u2081 \u0644\u0640 <img loading=\"lazy\" decoding=\"async\" width=\"12\" height=\"22\" class=\"wp-image-13404\" src=\"http:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-13.png\" srcset=\"https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-13.png 12w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-13-7x12.png 7w\" sizes=\"auto, (max-width: 12px) 100vw, 12px\" \/> .<\/p>\n<p style=\"text-align: justify;\">\u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0645\u062d\u062f\u062f\u0629 ( <img loading=\"lazy\" decoding=\"async\" width=\"30\" height=\"20\" class=\"wp-image-13405\" src=\"http:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-14.png\" srcset=\"https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-14.png 30w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-14-18x12.png 18w\" sizes=\"auto, (max-width: 30px) 100vw, 30px\" \/> )\u060c \u0648\u062d\u062f\u062f \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0645\u0635\u0637\u0646\u0639\u0629 \u0628\u0648\u0627\u0633\u0637\u0629<\/p>\n<p style=\"text-align: justify;\"><strong><em>x<\/em>* <sub>(n + p ) xp<\/sub> *<sub>(n + p ) <\/sub>( ).<\/strong><\/p>\n<p style=\"text-align: justify;\">\u0628\u0627\u0644\u062a\u0639\u0648\u064a\u0636 \u0641\u064a \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 (9) \u064a\u0646\u062a\u062c \u0645\u0627 \u064a\u0644\u064a<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" width=\"467\" height=\"57\" class=\"wp-image-13406\" src=\"http:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-15.png\" srcset=\"https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-15.png 467w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-15-300x37.png 300w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-15-18x2.png 18w\" sizes=\"auto, (max-width: 467px) 100vw, 467px\" \/><\/p>\n<p style=\"text-align: justify;\">\u0645\u0646 \u0627\u0644\u0645\u0647\u0645 \u0645\u0644\u0627\u062d\u0638\u0629 \u0623\u0646\u0647 \u0641\u064a \u0627\u0646\u062d\u062f\u0627\u0631 Elastic Net\u060c \u064a\u062a\u0645 \u0636\u0628\u0637 \u0627\u0644\u0625\u0639\u062f\u0627\u062f <img loading=\"lazy\" decoding=\"async\" width=\"11\" height=\"22\" class=\"wp-image-13407\" src=\"http:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-16.png\" srcset=\"https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-16.png 11w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-16-6x12.png 6w\" sizes=\"auto, (max-width: 11px) 100vw, 11px\" \/> = \u0635\u0641\u0631 \u064a\u0646\u062a\u062c \u0639\u0646\u0647\u0627 \u062d\u0644 \u0627\u0646\u062d\u062f\u0627\u0631 Ridge <img loading=\"lazy\" decoding=\"async\" width=\"11\" height=\"22\" class=\"wp-image-13408\" src=\"http:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-17.png\" srcset=\"https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-17.png 11w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-17-6x12.png 6w\" sizes=\"auto, (max-width: 11px) 100vw, 11px\" \/> =1 \u064a\u0646\u062a\u062c \u0639\u0646\u0647\u0627 \u062d\u0644 LASSO. \u0623\u062b\u0646\u0627\u0621 \u0627\u0644\u0625\u0639\u062f\u0627\u062f \u0639\u0642\u0648\u0628\u0629 \u0645\u062e\u062a\u0644\u0637\u0629 \u062a\u0645\u062b\u0644 \u0645\u0632\u064a\u062c\u064b\u0627 \u062e\u0627\u0644\u0635\u064b\u0627 \u0645\u0646 \u0645\u0642\u062f\u0631\u0627\u062a \u0627\u0646\u062d\u062f\u0627\u0631 Ridge \u0648LASSO.<\/p>\n<p style=\"text-align: justify;\">\u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u064a\u0624\u062f\u064a \u0636\u0628\u0637 \u0625\u0644\u0649 \u0625\u0646\u062a\u0627\u062c \u062d\u0644 OLS. \u0648\u0644\u0630\u0644\u0643 \u062a\u0648\u0641\u0631 \u0627\u0644\u0634\u0628\u0643\u0629 \u0627\u0644\u0645\u0631\u0646\u0629 (ENET) \u0625\u0637\u0627\u0631\u064b\u0627 \u0645\u0631\u0646\u064b\u0627 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0625\u062c\u0631\u0627\u0621\u0627\u062a Ridge \u0648LASSO \u0627\u0644\u0645\u0646\u062a\u0638\u0645\u0629<\/p>\n<p style=\"text-align: justify;\">(\u0627\u0646\u0638\u0631 Rish and Grabarnik, 2015, Helwig, 2017).<\/p>\n<p style=\"text-align: justify;\">\u064a\u0645\u0643\u0646 \u0631\u0624\u064a\u0629 \u0647\u0630\u0647 \u0627\u0644\u0645\u064a\u0632\u0627\u062a \u0627\u0644\u0645\u062b\u064a\u0631\u0629 \u0644\u0644\u0627\u0647\u062a\u0645\u0627\u0645 \u0628\u0648\u0636\u0648\u062d \u0641\u064a \u0634\u0643\u0644 4 (Helwig, 2017).<\/p>\n<p style=\"text-align: justify;\">\u0627\u0644\u0634\u0643\u0644 (4) \u0627\u0644\u0645\u062e\u0637\u0637\u0627\u062a \u0627\u0644\u0643\u0646\u062a\u0648\u0631\u064a\u0629 \u0644\u0645\u0642\u062f\u0631\u0627\u062a \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 Ridge \u0648 LASSO \u0648 Elastic Net<\/p>\n<p style=\"text-align: justify;\">\u064a\u0648\u0636\u062d \u0627\u0644\u0634\u0643\u0644 4 \u0645\u062f\u0649 \u0645\u0644\u0627\u0621\u0645\u0629 \u0647\u0646\u062f\u0633\u0629 \u0645\u062e\u0637\u0637\u0627\u062a \u0627\u0644\u0643\u0646\u062a\u0648\u0631 \u0644\u0643\u0644 \u0645\u0646 \u0627\u0646\u062d\u062f\u0627\u0631 Ridge \u0648 LASSO \u0648 Elastic Net \u0641\u064a \u0627\u0644\u0625\u062d\u062f\u0627\u062b\u064a\u0627\u062a \u062b\u0646\u0627\u0626\u064a\u0629 \u0627\u0644\u0623\u0628\u0639\u0627\u062f\u060c \u062d\u064a\u062b \u062a\u0643\u0648\u0646 \u0627\u0644\u0632\u0648\u0627\u064a\u0627 \u0627\u0644\u062d\u0627\u062f\u0629 \u0639\u0646\u062f \u0627\u0644\u0642\u0645\u0645 \u0648\u0627\u0644\u062d\u0648\u0627\u0641 \u0648\u0645\u062d\u062f\u0628\u0629 \u062a\u0645\u0627\u0645\u064b\u0627 \u0648\u0642\u0648\u0629 \u0627\u0644\u062a\u062d\u062f\u0628 \u0627\u0644\u062a\u064a \u062a\u062e\u062a\u0644\u0641 \u0645\u0639 \u0642\u064a\u0645\u0629 <img loading=\"lazy\" decoding=\"async\" width=\"12\" height=\"22\" class=\"wp-image-13409\" src=\"http:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-19.png\" srcset=\"https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-19.png 12w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-19-7x12.png 7w\" sizes=\"auto, (max-width: 12px) 100vw, 12px\" \/> .<\/p>\n<p style=\"text-align: justify;\"><strong>6.2 \u0645\u0642\u062f\u0631 \u0627\u0644\u0634\u0628\u0643\u0629 \u0627\u0644\u0645\u0631\u0646\u0629 \u0627\u0644\u062a\u0643\u064a\u0641\u064a Adaptive Elastic Net Estimator<\/strong><\/p>\n<p style=\"text-align: justify;\">\u062a\u0630\u0643\u0631 \u0623\u0646 Elastic Net Regression \u064a\u0646\u062a\u062c \u0646\u0645\u0627\u0630\u062c \u0627\u0646\u062d\u062f\u0627\u0631 \u062e\u0637\u064a \u0628\u0633\u064a\u0637\u0629 \u0623\u0648 \u0645\u062a\u0639\u062f\u062f\u0629 \u064a\u062a\u0645 \u062a\u063a\u0637\u064a\u062a\u0647\u0627 \u0628\u0623\u0633\u0644\u0648\u0628 L1 \u0648L2-norm. \u0648\u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0647\u064a \u062a\u0642\u0644\u064a\u0644 \u0627\u0644\u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0628\u0634\u0643\u0644 \u0641\u0639\u0627\u0644 \u0643\u0645\u0627 \u0647\u0648 \u0627\u0644\u062d\u0627\u0644 \u0641\u064a \u0627\u0646\u062d\u062f\u0627\u0631 Ridge \u0645\u0639 \u0639\u0642\u0648\u0628\u0629 \u0627\u0644\u062a\u062e\u0641\u064a\u0636 \u03bb<sub>2 <\/sub>P<sub>2 <\/sub>(B)) \u0648\u062a\u0639\u064a\u064a\u0646 \u0628\u0639\u0636 \u0627\u0644\u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0625\u0644\u0649 \u0627\u0644\u0635\u0641\u0631 \u0643\u0645\u0627 \u0647\u0648 \u0627\u0644\u062d\u0627\u0644 \u0641\u064a \u0627\u0646\u062d\u062f\u0627\u0631 LASSO \u0645\u0639 \u0639\u0642\u0648\u0628\u0629 \u0627\u0644\u062a\u062e\u0641\u064a\u0636 \u03bb<sub>1<\/sub>P<sub>1 <\/sub>(B) Zou and Hastie, 2005).<\/p>\n<p style=\"text-align: justify;\">\u064a\u0645\u0643\u0646 \u0636\u0628\u0637 \u0645\u0642\u062f\u0627\u0631 \u0627\u0644\u0639\u0642\u0648\u0628\u0629 \u0628\u0634\u0643\u0644 \u062c\u064a\u062f \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062b\u0648\u0627\u0628\u062a (\u03bb<sub>2 <\/sub>, \u03bb<sub>1 <\/sub>). \u0648\u0628\u0634\u0643\u0644 \u0623\u0643\u062b\u0631 \u062a\u062d\u062f\u064a\u062f\u064b\u0627\u060c \u064a\u0642\u0644\u0644 \u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0634\u0628\u0643\u0629 \u0627\u0644\u0645\u0631\u0646\u0629 \u0627\u0644\u062a\u0643\u064a\u0641\u064a\u0629 (AENET) \u0645\u0646 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 \u0627\u0644\u0645\u0639\u0627\u0642\u0628 \u0639\u0644\u064a\u0647\u0627 (PLS) \u0623\u0648 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0647\u062f\u0641<\/p>\n<p style=\"text-align: justify;\">\u0392<sub>AENET <\/sub> (11)<\/p>\n<p style=\"text-align: justify;\">\u0644\u0627\u062d\u0638 ( Tibshirani )1996 \u0623\u0646 \u0627\u0644\u0623\u062f\u0627\u0621 \u0627\u0644\u062a\u0646\u0628\u0624\u064a \u0627\u0644\u062a\u062c\u0631\u064a\u0628\u064a \u0644\u0640 LASSO \u064a\u0647\u064a\u0645\u0646 \u0639\u0644\u064a\u0647 \u0627\u0646\u062d\u062f\u0627\u0631 Ridge (\u0623\u064a \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062e\u0637\u064a \u0627\u0644\u0645\u0646\u062a\u0638\u0645 L2) \u0639\u0646\u062f\u0645\u0627 \u062a\u0643\u0648\u0646 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0642\u0644\u0629 \u0645\u0631\u062a\u0628\u0637\u0629 \u0628\u0634\u0643\u0644 \u0643\u0628\u064a\u0631\u060c \u0641\u064a \u062d\u064a\u0646 \u064a\u0646\u0639\u0643\u0633 \u0627\u0644\u0648\u0636\u0639 \u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 \u0647\u0646\u0627\u0643 \u0639\u062f\u062f \u0635\u063a\u064a\u0631 \u0646\u0633\u0628\u064a\u064b\u0627 \u0645\u0646 \u0623\u0643\u062b\u0631 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0642\u0644\u0629.<\/p>\n<p style=\"text-align: justify;\">\u0644\u0630\u0644\u0643\u060c \u0642\u062f \u064a\u0643\u0648\u0646 \u0645\u0646 \u0627\u0644\u0636\u0631\u0648\u0631\u064a \u0627\u0644\u062c\u0645\u0639 \u0628\u064a\u0646 \u0645\u0639\u064a\u0627\u0631\u064a L1 \u0648L2 \u0644\u062a\u062d\u0642\u064a\u0642 &#8220;\u0627\u0644\u0623\u0641\u0636\u0644 \u0641\u064a \u0643\u0644 \u0645\u0646 \u0645\u064a\u0632\u0627\u062a \u0627\u0646\u062d\u062f\u0627\u0631 Ridge \u0648LASSO.<\/p>\n<p style=\"text-align: justify;\">\u0628\u0627\u0641\u062a\u0631\u0627\u0636 \u0627\u0646<\/p>\n<p style=\"text-align: justify;\">\u062a\u0635\u0628\u062d \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 \u0627\u0644\u0645\u0639\u0627\u0642\u0628 \u0639\u0644\u064a\u0647\u0627 (PLS) \u0623\u0648 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u0648\u0636\u0648\u0639\u064a\u0629 \u0644\u0644\u0634\u0628\u0643\u0629 \u0627\u0644\u0645\u0631\u0646\u0629 \u0627\u0644\u062a\u0643\u064a\u0641\u064a\u0629 (AENET) \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 (12) \u0643\u0645\u0627 \u064a\u0644\u064a:<\/p>\n<p style=\"text-align: justify;\">\u062d\u064a\u062b \u0627\u0646 <img loading=\"lazy\" decoding=\"async\" width=\"44\" height=\"22\" class=\"wp-image-13410\" src=\"http:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-20.png\" srcset=\"https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-20.png 44w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-20-18x9.png 18w\" sizes=\"auto, (max-width: 44px) 100vw, 44px\" \/> \u0647\u064a \u0645\u0639\u0644\u0645\u0629 \u0627\u0644\u0639\u0642\u0648\u0628\u0629 (\u0623\u0648 \u0627\u0644\u0636\u0628\u0637) \u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0634\u0628\u0643\u0629 \u0627\u0644\u0645\u0631\u0646\u0629 \u0627\u0644\u062a\u0643\u064a\u0641\u064a\u0629 (AENET) \u0648 <img loading=\"lazy\" decoding=\"async\" width=\"11\" height=\"22\" class=\"wp-image-13411\" src=\"http:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-21.png\" srcset=\"https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-21.png 11w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-21-6x12.png 6w\" sizes=\"auto, (max-width: 11px) 100vw, 11px\" \/> \u0647\u064a \u0645\u0639\u0644\u0645\u0629 \u0627\u0644\u062e\u0644\u0637 \u0648\u062a\u062a\u062d\u0643\u0645 \u0641\u064a \u062a\u0623\u062b\u064a\u0631 L1 \u0648L2 \u0627\u0644\u062a\u064a \u062a\u0639\u0627\u0642\u0628 \u0639\u0644\u064a\u0647 ( Xiao and Xu, 2015).<\/p>\n<p style=\"text-align: justify;\">\u062a\u062a\u0645\u062a\u0639 \u0643\u0644 \u0645\u0646 \u062a\u0642\u062f\u064a\u0631\u0627\u062a LASSO \u0648Elastic Net \u0628\u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0643\u0628\u064a\u0631\u0629 \u063a\u064a\u0631 \u0635\u0641\u0631\u064a\u0629 \u0645\u0639 \u0627\u0646\u062d\u064a\u0627\u0632 \u0645\u0642\u0627\u0631\u0628 \u0644\u0627 \u064a\u0645\u0643\u0646 \u062a\u062c\u0627\u0647\u0644\u0647\u060c \u0648\u0644\u062d\u0644 \u0647\u0630\u0647 \u0627\u0644\u0645\u0634\u0643\u0644\u0629\u060c \u0627\u0642\u062a\u0631\u062d Zou (2006) \u0645\u0642\u062f\u0631 LASSO \u0627\u0644\u062a\u0643\u064a\u0641\u064a \u0627\u0644\u062a\u0627\u0644\u064a (ALASSO)<\/p>\n<p style=\"text-align: justify;\">\u00a0<\/p>\n<p style=\"text-align: justify;\">\u062d\u064a\u062b <em>w<sub>j<\/sub><\/em> \u0647\u064a \u0645\u0639\u0644\u0645\u0629 \u062a\u0631\u062c\u064a\u062d \u062a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a\u060c \u0648\u0627\u0644\u062a\u064a \u064a\u0645\u0643\u0646 \u062a\u0642\u062f\u064a\u0631\u0647\u0627 \u0628\u0648\u0627\u0633\u0637\u0629 <em>w<sub>j<\/sub> <\/em>= ( |<em>\u03b2<sub>j<\/sub><sup>ini <\/sup><\/em>|<sup>\u2212<\/sup><em><sup>\u03b3 <\/sup><\/em>) \u0648 <em>\u03b3<\/em> \u0647\u0648 \u062b\u0627\u0628\u062a \u0645\u0648\u062c\u0628. <em>\u03b2<sup>ini<\/sup><\/em> \u0639\u0628\u0627\u0631\u0629 \u0639\u0646 \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0646 \u0627\u0644\u0645\u0639\u0644\u0645\u0627\u062a \u0627\u0644\u0623\u0648\u0644\u064a\u0629\u060c \u0648\u0627\u0644\u062a\u064a \u064a\u0645\u0643\u0646 \u062d\u0633\u0627\u0628\u0647\u0627 \u0628\u0648\u0627\u0633\u0637\u0629 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 \u0627\u0644\u0639\u0627\u062f\u064a\u0629 (OLS) \u0623\u0648 \u0627\u0646\u062d\u062f\u0627\u0631 Ridge.<\/p>\n<p style=\"text-align: justify;\">\u064a\u0645\u0643\u0646 \u0627\u0644\u0646\u0638\u0631 \u0625\u0644\u0649 \u0627\u0644\u0634\u0628\u0643\u0629 \u0627\u0644\u0645\u0631\u0646\u0629 \u0627\u0644\u062a\u0643\u064a\u0641\u064a\u0629 (AENET) \u0639\u0644\u0649 \u0623\u0646\u0647\u0627 \u0645\u0632\u064a\u062c \u0645\u0646 \u0627\u0644\u0634\u0628\u0643\u0629 \u0627\u0644\u0645\u0631\u0646\u0629 (ENET) \u0648\u0627\u0646\u062d\u062f\u0627\u0631 LASSO \u0627\u0644\u062a\u0643\u064a\u0641\u064a (ALASSO).<\/p>\n<p style=\"text-align: justify;\">\u0633\u0646\u0642\u0648\u0645 \u0623\u0648\u0644\u0627\u064b \u0628\u062d\u0633\u0627\u0628 \u062a\u0642\u062f\u064a\u0631 \u0627\u0644\u0634\u0628\u0643\u0629 \u0627\u0644\u0645\u0631\u0646\u0629) <strong>Elastic Net<\/strong> <strong>ENET<\/strong>) \u0627\u0644\u0645\u062d\u062f\u062f\u0629 \u0643\u0645\u0627 \u0641\u064a \u0627\u0644\u0633\u0627\u0628\u0642\u060c \u062b\u0645 \u0646\u0642\u0648\u0645 \u0628\u0628\u0646\u0627\u0621 \u0627\u0644\u0623\u0648\u0632\u0627\u0646 \u0627\u0644\u062a\u0643\u064a\u0641\u064a\u0629 \u0628\u0648\u0627\u0633\u0637\u0629<\/p>\n<p style=\"text-align: justify;\">(15) <img loading=\"lazy\" decoding=\"async\" width=\"399\" height=\"47\" class=\"wp-image-13412\" src=\"http:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-22.png\" srcset=\"https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-22.png 399w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-22-300x35.png 300w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-22-18x2.png 18w\" sizes=\"auto, (max-width: 399px) 100vw, 399px\" \/><\/p>\n<p style=\"text-align: justify;\">\u062d\u064a\u062b \u03b3 \u0644\u0627 \u064a\u0632\u0627\u0644 \u062b\u0627\u0628\u062a\u064b\u0627 \u0645\u0648\u062c\u0628\u064b\u0627. \u0644\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u062a\u0642\u062f\u064a\u0631 \u0627\u0644\u0634\u0628\u0643\u0629 \u0627\u0644\u0645\u0631\u0646\u0629 \u0627\u0644\u062a\u0643\u064a\u0641\u064a\u0629 (AENET)\u060c \u0633\u0646\u062d\u0644 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u062d\u0633\u064a\u0646 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p style=\"text-align: justify;\">(16) <img loading=\"lazy\" decoding=\"async\" width=\"515\" height=\"69\" class=\"wp-image-13413\" src=\"http:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-23.png\" srcset=\"https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-23.png 515w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-23-300x40.png 300w, https:\/\/www.hnjournal.net\/wp-content\/uploads\/2025\/05\/word-image-13359-23-18x2.png 18w\" sizes=\"auto, (max-width: 515px) 100vw, 515px\" \/><\/p>\n<p style=\"text-align: justify;\">\u062a\u0636\u0645\u0646 \u0627\u0644\u0634\u0628\u0643\u0629 \u0627\u0644\u0645\u0631\u0646\u0629 \u0627\u0644\u062a\u0643\u064a\u0641\u064a\u0629) <strong>Adaptive Elastic Net<\/strong> <strong>AENET)<\/strong> \u0623\u064a\u0636\u064b\u0627 \u0627\u062a\u0633\u0627\u0642 \u0627\u0644\u0627\u062e\u062a\u064a\u0627\u0631 \u0627\u0644\u0645\u062a\u063a\u064a\u0631 \u0648\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062d\u0627\u0644\u0629 \u0627\u0644\u0637\u0628\u064a\u0639\u064a\u0629 \u0627\u0644\u0645\u0642\u0627\u0631\u0628\u0629 \u0645\u062b\u0644 <strong>Adaptive LASSO ) ALASSO)<\/strong> \u0648\u064a\u0645\u0643\u0646\u0647\u0627 \u0627\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a \u0639\u0646 \u0637\u0631\u064a\u0642 \u0625\u0636\u0627\u0641\u0629 \u0634\u0631\u0648\u0637 \u062a\u0646\u0638\u064a\u0645 L2.<\/p>\n<p style=\"text-align: justify;\"><strong><em>3. \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629<\/em><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>1.3 \u0645\u0642\u062f\u0645\u0629<\/strong><\/p>\n<p style=\"text-align: justify;\">\u062a\u0645 \u062a\u062e\u0635\u064a\u0635 \u0647\u0630\u0627 \u0627\u0644\u0641\u0635\u0644 \u0644\u0645\u0642\u0627\u0631\u0646\u0629 \u0623\u062f\u0627\u0621 \u0627\u0644\u0645\u0642\u062f\u0631\u0627\u062a \u0627\u0644\u062e\u0645\u0633\u0629 \u0627\u0644\u0645\u0642\u062a\u0631\u062d\u0629: \u0648\u0647\u064a: \u0631\u064a\u062f\u062c (Ridge)\u060c \u0648\u0627\u0644\u0644\u0627\u0633\u0648 (Lasso)\u060c \u0648\u0627\u0644\u0634\u0628\u0643\u0629 \u0627\u0644\u0645\u0631\u0646\u0629 (\u064fElastic Net)\u060c \u0648\u0627\u0644\u0644\u0627\u0633\u0648 \u0627\u0644\u062a\u0643\u064a\u0641\u064a (Adaptive Lasso)\u060c \u0648\u0645\u0642\u062f\u0631\u0627\u062a \u0627\u0644\u0634\u0628\u0643\u0629 \u0627\u0644\u0645\u0631\u0646\u0629 \u0627\u0644\u062a\u0643\u064a\u0641\u064a\u0629 (Adaptive Elastic Net) \u0627\u0644\u062a\u064a \u0627\u0633\u062a\u062e\u062f\u0645\u062a \u0641\u064a \u0645\u0639\u0627\u0644\u062c\u0629 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a \u0648\u0645\u0634\u0643\u0644\u0629 \u062a\u0639\u062f\u062f \u0627\u0644\u0627\u0628\u0639\u0627\u062f \u0639\u0628\u0631 \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629. \u0645\u0646 \u0623\u062c\u0644 \u0627\u0644\u062a\u0639\u0631\u0641 \u0628\u0634\u0643\u0644 \u0623\u0641\u0636\u0644 \u0639\u0644\u0649 \u062e\u0635\u0627\u0626\u0635 \u0645\u0642\u062f\u0631\u0627\u062a \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062c\u0632\u0627\u0626\u064a\u0629 \u0648\u0628\u0639\u0636 \u0628\u062f\u0627\u0626\u0644\u0647\u060c \u0642\u0645\u0646\u0627 \u0628\u062d\u0633\u0627\u0628 \u0645\u062c\u0645\u0648\u0639\u062a\u064a\u0646 \u0645\u0646 \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629. \u064a\u062a\u0645 \u0648\u0635\u0641 \u0627\u0644\u0625\u062c\u0631\u0627\u0621\u0627\u062a \u0627\u0644\u062f\u0642\u064a\u0642\u0629 \u0641\u064a \u0627\u0644\u0642\u0633\u0645 \u0627\u0644\u062a\u0627\u0644\u064a. \u062a\u062a\u0636\u0645\u0646 \u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u062a\u0642\u062f\u064a\u0631\u0627\u062a \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062c\u0632\u0627\u0626\u064a\u0629. \u0644\u0642\u062f \u0642\u0645\u0646\u0627 \u0628\u062a\u0636\u0645\u064a\u0646 \u0646\u0647\u062c OLS \u0630\u064a \u0627\u0644\u0635\u0644\u0629 \u0639\u0644\u0649 \u0627\u0644\u0631\u063a\u0645 \u0645\u0646 \u062d\u0642\u064a\u0642\u0629 \u0623\u0646\u0647 \u064a\u064f\u0633\u062a\u062e\u062f\u0645 \u0628\u0634\u0643\u0644 \u0623\u0633\u0627\u0633\u064a \u0644\u062a\u0642\u062f\u064a\u0631 \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u0639\u0646\u062f\u0645\u0627 \u0644\u0627 \u064a\u0643\u0648\u0646 \u0645\u0634\u0643\u0644\u0629 \u062a\u0639\u062f\u062f \u0627\u0644\u0627\u0628\u0639\u0627\u062f \u0645\u0648\u062c\u0648\u062f\u0629.<\/p>\n<p style=\"text-align: justify;\">\u0628\u0634\u0643\u0644 \u0639\u0627\u0645\u060c \u062f\u0631\u0627\u0633\u0627\u062a \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0647\u064a \u0641\u064a \u0627\u0644\u063a\u0627\u0644\u0628 \u062a\u0642\u0646\u064a\u0629 \u0644\u0625\u062c\u0631\u0627\u0621 \u062a\u062c\u0627\u0631\u0628 \u0639\u0644\u0649 \u0646\u0645\u0648\u0630\u062c. \u0639\u0644\u0649 \u0639\u0643\u0633 \u0627\u0644\u0637\u0631\u0642 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629\u061b \u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u062f\u0642\u064a\u0642\u0629 \u0648\u0633\u0647\u0644\u0629 \u0627\u0644\u0641\u0647\u0645 \u0648\u0644\u0643\u0646 \u0641\u0642\u0637 \u0641\u064a \u062d\u0627\u0644\u0629 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647\u0627 \u0628\u0634\u0643\u0644 \u0645\u0646\u0627\u0633\u0628. \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0623\u0637\u0631\u0648\u062d\u0629\u060c \u062a\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0623\u062c\u0647\u0632\u0629 \u0627\u0644\u0643\u0645\u0628\u064a\u0648\u062a\u0631 \u0627\u0644\u062a\u064a \u064a\u062a\u0645 \u0625\u0646\u0634\u0627\u0624\u0647\u0627 \u0643\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0635\u0637\u0646\u0627\u0639\u064a\u0629 \u0628\u062f\u0644\u0627\u064b \u0645\u0646 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u062d\u0642\u064a\u0642\u064a\u0629. \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0647\u0630\u0647 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0627\u0635\u0637\u0646\u0627\u0639\u064a\u0629 \u062a\u0645\u0627\u0645\u064b\u0627 \u0645\u062b\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u062d\u0642\u064a\u0642\u064a\u0629 \u0644\u0625\u0646\u062a\u0627\u062c \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0642\u0644\u0629 \u0648\u0627\u0644\u062a\u0627\u0628\u0639\u0629 \u0648\u0645\u0642\u0627\u0631\u0646\u0629 \u0646\u062a\u0627\u0626\u062c \u0627\u0644\u0645\u0642\u062f\u0631\u0627\u062a \u0627\u0644\u0645\u0642\u062a\u0631\u062d\u0629 \u0646\u0638\u0631\u064b\u0627 \u0644\u0623\u0646 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0627\u0635\u0637\u0646\u0627\u0639\u064a\u0629 \u062a\u062d\u062a \u0633\u064a\u0637\u0631\u0629 \u0627\u0644\u0628\u0627\u062d\u062b\u060c \u0648\u063a\u0627\u0644\u0628\u064b\u0627 \u0645\u0627 \u064a\u0643\u0648\u0646 \u0627\u0644\u0623\u062f\u0627\u0621 \u0627\u0644\u0646\u0638\u0631\u064a \u0627\u0644\u0625\u062d\u0635\u0627\u0626\u064a \u0645\u0639\u0631\u0648\u0641\u064b\u0627. \u062a\u0645 \u0625\u062c\u0631\u0627\u0621 \u062c\u0645\u064a\u0639 \u0627\u0644\u062d\u0633\u0627\u0628\u0627\u062a \u0648\u0627\u0644\u0631\u0633\u0648\u0645\u0627\u062a \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0623\u0637\u0631\u0648\u062d\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0632\u0645\u0629 \u0627\u0644\u0628\u0631\u0627\u0645\u062c R\u060c \u0648\u0627\u0644\u062a\u064a \u062a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0627\u0644\u0644\u063a\u0629 \u0627\u0644\u0625\u062d\u0635\u0627\u0626\u064a\u0629R<\/p>\n<p style=\"text-align: justify;\">(R Language and environment for Statistical computing, 2015).<\/p>\n<p style=\"text-align: justify;\">\u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u0644\u062f\u064a\u0646\u0627 \u062b\u0642\u0629 \u0641\u064a \u0646\u062a\u0627\u0626\u062c\u0646\u0627 \u0627\u0644\u062a\u064a \u062a\u0639\u062f \u0645\u0641\u064a\u062f\u0629 \u062c\u062f\u064b\u0627 \u0641\u064a \u062a\u0642\u064a\u064a\u0645 \u0627\u0644\u0623\u062f\u0627\u0621 \u0627\u0644\u0639\u0645\u0644\u064a \u0644\u0644\u0645\u0642\u062f\u0631\u0627\u062a \u0627\u0644\u062e\u0645\u0633\u0629 \u0627\u0644\u0645\u0642\u062a\u0631\u062d\u0629 \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u062a\u064a \u0646\u0633\u062a\u062e\u062f\u0645\u0647\u0646 \u0644\u062d\u0644 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a \u0648 \u0645\u0634\u0643\u0644\u0629 \u062a\u0639\u062f\u062f \u0627\u0644\u0627\u0628\u0639\u0627\u062f.<\/p>\n<p style=\"text-align: justify;\"><strong>2.3 \u0648\u0635\u0641 \u062a\u062c\u0631\u0628\u0629 \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 <\/strong><\/p>\n<p style=\"text-align: justify;\">\u0641\u064a \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0647\u0630\u0647\u060c \u062a\u0645\u062a \u0645\u0642\u0627\u0631\u0646\u0629 \u062a\u0642\u062f\u064a\u0631\u0627\u062a \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062c\u0632\u0627\u0626\u064a\u0629 \u0627\u0644\u062e\u0645\u0633\u0629 \u0627\u0644\u0645\u0642\u062a\u0631\u062d\u0629 \u0645\u0639 \u0628\u0639\u0636\u0647\u0627 \u0627\u0644\u0628\u0639\u0636 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062e\u064a\u0627\u0631\u0627\u062a \u0645\u062e\u062a\u0644\u0641\u0629 \u0645\u0646 \u0627\u0644\u0627\u0631\u062a\u0628\u0627\u0637 \u03c1 = (0.00 \u0648 0.10 \u0648 0.25 \u0648 0.50 \u0648 0.75 \u0648 0.90) \u0628\u064a\u0646 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u062a\u0648\u0636\u064a\u062d\u064a\u0629. \u0648\u0642\u062f \u062a\u0645 \u0627\u0644\u0642\u064a\u0627\u0645 \u0628\u0630\u0644\u0643 \u0645\u0646 \u0623\u062c\u0644 \u062a\u062d\u062f\u064a\u062f \u0628\u0639\u0636 \u0627\u0644\u0645\u0632\u0627\u064a\u0627 \u0627\u0644\u0634\u0627\u0626\u0639\u0629 \u0644\u0645\u0642\u062f\u0631\u0627\u062a \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062c\u0632\u0627\u0626\u064a\u0629 \u0627\u0644\u062a\u064a \u064a\u062a\u0645 \u0627\u0644\u0627\u0633\u062a\u0634\u0647\u0627\u062f \u0628\u0647\u0627 \u0628\u0634\u0643\u0644 \u0623\u0641\u0636\u0644\u060c \u0645\u062b\u0644 \u0623\u064a\u0647\u0627 \u064a\u0639\u0645\u0644 \u0628\u0634\u0643\u0644 \u0623\u0641\u0636\u0644 \u0639\u0646\u062f\u0645\u0627 \u062a\u0643\u0648\u0646 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u062a\u0648\u0636\u064a\u062d\u064a\u0629 \u0641\u064a \u0646\u0645\u0648\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0645\u062a\u0631\u0627\u0628\u0637\u0629 \u0628\u0642\u0648\u0629. \u062a\u0645 \u062a\u0635\u0646\u064a\u0641 \u0627\u0644\u062f\u0631\u0627\u0633\u0629 \u0625\u0644\u0649 \u0646\u0645\u0637\u064a\u0646 \u0645\u062e\u062a\u0644\u0641\u064a\u0646 \u0643\u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p style=\"text-align: justify;\">\u0627\u0644\u0646\u0645\u0637 1: \u062a\u0648\u0632\u064a\u0639 \u062d\u062f \u0627\u0644\u062e\u0637\u0623 \u064a\u062a\u0628\u0639 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0637\u0628\u064a\u0639\u064a\u060c<\/p>\n<p style=\"text-align: justify;\">\u0627\u0644\u0646\u0645\u0637 2: \u062a\u0648\u0632\u064a\u0639 \u062d\u062f \u0627\u0644\u062e\u0637\u0623 \u0644\u0627 \u064a\u062a\u0628\u0639 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0637\u0628\u064a\u0639\u064a.<\/p>\n<p style=\"text-align: justify;\">\u0641\u064a \u0643\u0644 \u0646\u0645\u0637\u060c \u0639\u062f\u0629 \u0627\u062e\u062a\u064a\u0627\u0631\u0627\u062a \u0644\u0639\u062f\u062f \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u062a\u0648\u0636\u064a\u062d\u064a\u0629 P = (20 \u064850 \u0648100). \u0643\u0627\u0646\u062a \u0623\u062d\u062c\u0627\u0645 \u0627\u0644\u0639\u064a\u0646\u0629 n \u0627\u0644\u062a\u064a \u062a\u0645 \u0627\u0644\u0646\u0638\u0631 \u0641\u064a\u0647\u0627 \u0635\u063a\u064a\u0631\u0629 \u0627\u0644\u062d\u062c\u0645 \u0648\u0645\u062a\u0648\u0633\u0637 \u0627\u0644\u062d\u062c\u0645 \u0648\u0643\u0628\u064a\u0631 \u0627\u0644\u062d\u062c\u0645 \u0648\u0643\u0627\u0646 \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u0639\u0644\u0649 \u0634\u0643\u0644 Y.<\/p>\n<p style=\"text-align: justify;\">\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0646\u0648\u0639\u064a\u0646 \u0645\u062e\u062a\u0644\u0641\u064a\u0646 \u0645\u0646 \u0627\u0644\u062a\u0648\u0632\u064a\u0639\u0627\u062a \u0627\u0644\u0647\u0627\u0645\u0634\u064a\u0629 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u062d\u062f \u062e\u0637\u0623 \u0647\u0627\u0645\u0634\u064a\u0646 \u0647\u0645\u0627: \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a Normal distribution.\u060c \u0648\u062a\u0648\u0632\u064a\u0639 (3)t (Heavy tailed t-distribution) .<\/p>\n<p style=\"text-align: justify;\"><strong>1.2.3 \u0627\u0644\u0645\u0644\u062e\u0635 \u0627\u0644\u0639\u062f\u062f\u064a \u0648\u0627\u0644\u0631\u0633\u0648\u0645\u0627\u062a \u0627\u0644\u0628\u064a\u0627\u0646\u064a\u0629<\/strong><\/p>\n<p style=\"text-align: justify;\">\u0628\u0627\u0633\u062a\u0639\u0645\u0627\u0644 \u062e\u064a\u0627\u0631\u0627\u062a \u0645\u062e\u062a\u0644\u0641\u0629 \u0645\u0646 \u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u0627\u0631\u062a\u0628\u0627\u0637\u0627\u062a \u03c1 = (0.00 \u06480.10 \u06480.25 \u06480.50 \u06480.75 \u06480.90) \u0628\u064a\u0646 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u062a\u0648\u0636\u064a\u062d\u064a\u0629 \u0648\u062b\u0644\u0627\u062b\u0629 \u0623\u062d\u062c\u0627\u0645 \u0627\u0644\u0639\u064a\u0646\u0627\u062a \u0627\u0644\u0635\u063a\u064a\u0631\u0629 (n = 10 \u064814 \u064818) \u0639\u0646\u062f\u0645\u0627 \u064a\u062a\u0645 \u062a\u062d\u062f\u064a\u062f \u0639\u062f\u062f \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0642\u0644\u0629 \u0628\u0640 20. \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0623\u062d\u062c\u0627\u0645 \u0627\u0644\u0639\u064a\u0646\u0629 \u0627\u0644\u0645\u062a\u0648\u0633\u0637\u0629 (n = 20 \u064830 \u064840) \u0639\u0646\u062f\u0645\u0627 \u064a\u062a\u0645 \u062a\u062d\u062f\u064a\u062f \u0639\u062f\u062f \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0642\u0644\u0629 \u0628\u0640 50. \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0623\u062d\u062c\u0627\u0645 \u0627\u0644\u0639\u064a\u0646\u0627\u062a \u0627\u0644\u0643\u0628\u064a\u0631\u0629 (n = 60 \u064870 \u064880) \u0639\u0646\u062f\u0645\u0627 \u064a\u062a\u0645 \u062a\u062d\u062f\u064a\u062f \u0639\u062f\u062f \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0642\u0644\u0629 \u0628\u0640 100 \u0648\u0643\u0630\u0644\u0643 \u062a\u0648\u0632\u064a\u0639\u0627\u062a \u0627\u0644\u0623\u062e\u0637\u0627\u0621 \u0627\u0644\u0647\u0627\u0645\u0634\u064a\u0629 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629 \u0644\u0643\u0644 1000 \u0639\u0645\u0644\u064a\u0629 \u0645\u062d\u0627\u0643\u0627\u0629 \u0645\u062e\u062a\u0644\u0641\u0629 \u0628\u0634\u0643\u0644 \u0645\u0633\u062a\u0642\u0644\u060c \u064a\u0639\u0637\u064a \u0643\u0644 \u0645\u0646\u0647\u0627 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0627\u0644\u0645\u0628\u064a\u0646\u0629 \u0641\u064a \u0645\u062e\u0637\u0637\u0627\u062a \u0627\u0644\u0635\u0646\u062f\u0648\u0642 (\u0634\u0643\u0644 3 \u0648\u0634\u0643\u0644 4). \u0646\u062a\u0627\u0626\u062c \u0627\u0644\u0645\u062a\u0648\u0633\u0637\u0627\u062a \u0648\u0646\u062a\u0627\u0626\u062c \u0627\u0644\u0627\u0646\u062d\u0631\u0627\u0641\u0627\u062a \u0627\u0644\u0645\u0639\u064a\u0627\u0631\u064a\u0629 \u0644\u0645\u062a\u0648\u0633\u0637 \u200b\u200b\u0627\u0644\u062e\u0637\u0623 \u0627\u0644\u062a\u0631\u0628\u064a\u0639\u064a (MSE) \u0627\u0644\u0630\u064a \u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0645\u0642\u062f\u0631\u0627\u062a \u0627\u0644\u0633\u062a\u0629 \u0627\u0644\u0645\u0642\u062a\u0631\u062d\u0629 \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062f\u0631\u0627\u0633\u0629.<\/p>\n<p style=\"text-align: justify;\"><strong>\u062a\u062c\u0631\u0628\u0629 \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0627\u0644\u0627\u0648\u0644\u064a: \u062d\u062f \u0627\u0644\u062e\u0637\u0627\u0621 \u064a\u062a\u0628\u0639 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a<\/strong><\/p>\n<table>\n<tbody>\n<tr>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u0627\u0644\u0634\u0643\u0644 (5) <em> \u064a\u0648\u0636\u062d \u0645\u062e\u0637\u0637\u0627\u062a \u0627\u0644\u0635\u0646\u062f\u0648\u0642 \u0644\u0643\u064a\u0641\u0647 \u062a\u062a\u0623\u062b\u0631 \u062e\u064a\u0627\u0631\u0627\u062a \u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u0627\u0631\u062a\u0628\u0627\u0637 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629 \u0639\u0644\u0649 \u0627\u0644\u0645\u062a\u0648\u0633\u0637 \u200b\u200b(\u0627\u0644\u0627\u0646\u062d\u0631\u0627\u0641 \u0627\u0644\u0645\u0639\u064a\u0627\u0631\u064a) \u0644\u0642\u064a\u0645\u0629 MSE \u0644\u0644\u0645\u0642\u062f\u0631\u0627\u062a \u0627\u0644\u0633\u062a\u0629 \u0627\u0644\u0645\u0642\u062a\u0631\u062d\u0629 (OLS \u0648 Ridge \u0648 Lasso \u0648 Elastic Net \u0648 Adaptive Lasso \u0648 Adaptive Elastic Net) , 50 , 100 p = 20 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0646\u0645\u0637 1.<\/em><\/p>\n<p style=\"text-align: justify;\"><strong>\u062a\u062c\u0631\u0628\u0629 \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0627\u0644\u062b\u0627\u0646\u064a\u0629: \u062d\u062f \u0627\u0644\u062e\u0637\u0627\u0621 \u0644\u0627 \u064a\u062a\u0628\u0639 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a<\/strong><\/p>\n<table>\n<tbody>\n<tr>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<tr>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<td>\u00a0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">\u0627\u0644\u0634\u0643\u0644 (6) <em> \u064a\u0648\u0636\u062d \u0645\u062e\u0637\u0637\u0627\u062a \u0627\u0644\u0635\u0646\u062f\u0648\u0642 \u0644\u0643\u064a\u0641\u0647 \u062a\u062a\u0623\u062b\u0631 \u062e\u064a\u0627\u0631\u0627\u062a \u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u0627\u0631\u062a\u0628\u0627\u0637 \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629 \u0639\u0644\u0649 \u0627\u0644\u0645\u062a\u0648\u0633\u0637 \u200b\u200b(\u0627\u0644\u0627\u0646\u062d\u0631\u0627\u0641 \u0627\u0644\u0645\u0639\u064a\u0627\u0631\u064a) \u0644\u0642\u064a\u0645\u0629 MSE \u0644\u0644\u0645\u0642\u062f\u0631\u0627\u062a \u0627\u0644\u0633\u062a\u0629 \u0627\u0644\u0645\u0642\u062a\u0631\u062d\u0629 (OLS \u0648 Ridge \u0648 Lasso \u0648 Elastic Net \u0648 Adaptive Lasso \u0648 Adaptive Elastic Net) , 50 , 100 p = 20 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0646\u0645\u0637 2.<\/em><\/p>\n<p style=\"text-align: justify;\"><strong>4. \u0645\u0646\u0627\u0642\u0634\u0629 \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629<\/strong><\/p>\n<p style=\"text-align: justify;\">\u0627\u0644\u063a\u0631\u0636 \u0645\u0646 \u0647\u0630\u0627 \u0627\u0644\u0642\u0633\u0645 \u0647\u0648 \u062a\u0644\u062e\u064a\u0635 \u0641\u0639\u0627\u0644\u064a\u0629 \u0627\u0644\u062a\u0642\u062f\u064a\u0631 \u0648\u0627\u0644\u0627\u062a\u0633\u0627\u0642 \u0628\u064a\u0646 \u0645\u0642\u062f\u0631\u0627\u062a Ridge \u0648LASSO \u0648Elastic Net \u0648Adaptive Lasso \u0648Adaptive Elastic Net \u0627\u0644\u062a\u064a \u064a\u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647\u0627 \u0644\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0645\u0634\u0643\u0644\u0629 &#8220;\u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a&#8221; \u0648\u0645\u0634\u0643\u0644\u0629 \u201c\u062a\u0639\u062f\u062f \u0627\u0644\u0627\u0628\u0639\u0627\u062f&#8221; \u0648\u062d\u0644\u0647\u0627 \u0639\u0646\u062f\u0645\u0627 \u062a\u0643\u0648\u0646 \u0627\u0644\u0623\u062e\u0637\u0627\u0621 \u0625\u0645\u0627 \u0645\u0648\u0632\u0639\u0629 \u0628\u0634\u0643\u0644 \u0637\u0628\u064a\u0639\u064a \u0623\u0648 \u0645\u0648\u0632\u0639\u0629 \u0628\u0634\u0643\u0644 \u063a\u064a\u0631 \u0637\u0628\u064a\u0639\u064a.<\/p>\n<p style=\"text-align: justify;\"><strong>1.4 \u0627\u0644\u0646\u0645\u0637 \u0627\u0644\u0623\u0648\u0644: \u062d\u062f \u0627\u0644\u062e\u0637\u0623 \u0645\u0648\u0632\u0639 \u062a\u0648\u0632\u064a\u0639\u0627\u064b \u0637\u0628\u064a\u0639\u064a\u0627\u064b<\/strong><\/p>\n<p style=\"text-align: justify;\">\u0641\u064a \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0627\u0644\u0623\u0648\u0644\u0649\u060c \u062a\u0645 \u0627\u0644\u062a\u062e\u0637\u064a\u0637 \u0641\u064a \u062d\u0627\u0644\u0629 \u0648\u062c\u0648\u062f \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a \u0648\u0645\u0634\u0643\u0644\u0629 \u062a\u0639\u062f\u062f \u0627\u0644\u0627\u0628\u0639\u0627\u062f \u0628\u064a\u0646 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u062a\u0648\u0636\u064a\u062d\u064a\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0633\u062a\u0629 \u0645\u0642\u062f\u0631\u0627\u062a (OLS\u060c Ridge\u060c LASSO\u060c Elastic Net\u060c Adaptive Lasso\u060c (Adaptive Elastic Net \u0648\u062a\u0645 \u0625\u062c\u0631\u0627\u0621 \u0627\u0644\u0645\u0642\u0627\u0631\u0646\u0627\u062a \u0641\u064a\u0645\u0627 \u0628\u064a\u0646\u0647\u0627 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0645\u062a\u0648\u0633\u0637\u0629 \u0644\u0640 (MSE) \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0642\u064a\u0645 \u0627\u0644\u0627\u0646\u062d\u0631\u0627\u0641\u0627\u062a \u0627\u0644\u0645\u0639\u064a\u0627\u0631\u064a\u0629 \u0627\u0644\u0645\u0642\u0627\u0628\u0644\u0629 \u0644\u0647\u0627 \u0639\u0644\u0649 \u0627\u0641\u062a\u0631\u0627\u0636 \u0623\u0646 \u062d\u062f\u0648\u062f \u0627\u0644\u062e\u0637\u0623 \u0645\u0648\u0632\u0639\u0629 \u0628\u0634\u0643\u0644 \u0637\u0628\u064a\u0639\u064a. \u062a\u0645 \u0627\u0644\u062a\u0648\u0635\u0644 \u0625\u0644\u0649 \u0627\u0644\u0646\u0642\u0627\u0637 \u0627\u0644\u062b\u0644\u0627\u062b \u0627\u0644\u0645\u062b\u064a\u0631\u0629 \u0644\u0644\u0627\u0647\u062a\u0645\u0627\u0645 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p style=\"text-align: justify;\">1- \u064a\u0639\u0637\u064a \u0645\u0642\u062f\u0631OLS \u062f\u0627\u0626\u0645\u0627 \u0642\u064a\u0645 MSE \u0643\u0628\u064a\u0631\u0629 \u062c\u062f\u064b\u0627 \u0628\u0633\u0628\u0628 \u0648\u062c\u0648\u062f \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a.<\/p>\n<p style=\"text-align: justify;\">2- \u064a\u0639\u062a\u0628\u0631 \u0627\u0646\u062d\u062f\u0627\u0631 \u0631\u064a\u062f\u062c Ridge \u0623\u062d\u062f \u0623\u0643\u062b\u0631 \u0625\u062c\u0631\u0627\u0621\u0627\u062a \u0627\u0644\u062a\u0642\u062f\u064a\u0631 \u0634\u064a\u0648\u0639\u064b\u0627\u060c \u0639\u0644\u0649 \u0627\u0644\u0631\u063a\u0645 \u0645\u0646 \u0627\u0644\u062c\u062f\u0644 \u062d\u0648\u0644\u0647\u060c \u0644\u062d\u0644 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0627\u0644\u062e\u0637\u064a\u0629 \u0627\u0644\u0645\u062a\u0639\u062f\u062f\u0629. \u062a\u0646\u062f\u0631\u062c \u0627\u0644\u0625\u062c\u0631\u0627\u0621\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u0645\u062a \u0645\u0646\u0627\u0642\u0634\u062a\u0647\u0627 \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0636\u0645\u0646 \u0646\u0648\u0639 \u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u062a\u0642\u062f\u064a\u0631 \u0627\u0644\u0645\u062a\u062d\u064a\u0632\u0629. \u0648\u0647\u064a \u062a\u0633\u062a\u0646\u062f \u0625\u0644\u0649 \u0647\u0630\u0647 \u0627\u0644\u0641\u0643\u0631\u0629: \u0639\u0644\u0649 \u0627\u0644\u0631\u063a\u0645 \u0645\u0646 \u0623\u0646 \u0645\u0642\u062f\u0631 OLS \u064a\u0639\u0637\u064a \u0623\u0641\u0636\u0644 \u0645\u0642\u062f\u0631 \u062e\u0637\u064a \u063a\u064a\u0631 \u0645\u062a\u062d\u064a\u0632 (Blue)\u060c \u0625\u0644\u0627 \u0623\u0646\u0647 \u0644\u0627 \u064a\u0648\u062c\u062f \u062d\u062f \u0623\u0639\u0644\u0649 \u0644\u062a\u0628\u0627\u064a\u0646 \u0627\u0644\u0645\u0642\u062f\u0631 \u0648\u0642\u062f \u064a\u0624\u062f\u064a \u0648\u062c\u0648\u062f \u0639\u0644\u0627\u0642\u0629 \u062e\u0637\u064a\u0629 \u0645\u062a\u0639\u062f\u062f\u0629 \u0625\u0644\u0649 \u0625\u0646\u062a\u0627\u062c \u062a\u0628\u0627\u064a\u0646 \u0643\u0628\u064a\u0631. \u0644\u0630\u0644\u0643\u060c \u064a\u0645\u0643\u0646 \u0644\u0644\u0645\u0631\u0621 \u0623\u0646 \u064a\u062a\u0635\u0648\u0631 \u0623\u0646\u0647\u060c \u0641\u064a \u0638\u0644 \u0634\u0631\u0637 \u0627\u0644\u062a\u0639\u062f\u062f\u064a\u0629 \u0627\u0644\u062e\u0637\u064a\u0629\u060c \u064a\u062c\u0628 \u062f\u0641\u0639 \u062b\u0645\u0646 \u0628\u0627\u0647\u0638 \u0645\u0642\u0627\u0628\u0644 \u062e\u0627\u0635\u064a\u0629 \u0639\u062f\u0645 \u0627\u0644\u062a\u062d\u064a\u0632 \u0627\u0644\u062a\u064a \u064a\u0646\u062c\u0632\u0647\u0627 \u0627\u0644\u0628\u0627\u062d\u062b \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0646\u062d\u062f\u0627\u0631 \u0631\u064a\u062f\u062c Ridge \u064a\u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062a\u0642\u062f\u064a\u0631 \u0627\u0644\u0645\u062a\u062d\u064a\u0632 \u0644\u062a\u062d\u0642\u064a\u0642 \u0627\u0646\u062e\u0641\u0627\u0636 \u0643\u0628\u064a\u0631 \u0641\u064a \u0627\u0644\u062a\u0628\u0627\u064a\u0646 \u0645\u0639 \u0632\u064a\u0627\u062f\u0629 \u0645\u0635\u0627\u062d\u0628\u0629 \u0641\u064a \u0627\u0633\u062a\u0642\u0631\u0627\u0631 \u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631. \u062a\u0635\u0628\u062d \u0627\u0644\u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0645\u062a\u062d\u064a\u0632\u0629 \u0648\u064a\u0643\u0648\u0646 \u0627\u0646\u062e\u0641\u0627\u0636 \u0627\u0644\u062a\u0628\u0627\u064a\u0646 \u0623\u0643\u0628\u0631 \u0645\u0646 \u0627\u0644\u062a\u062d\u064a\u0632 \u0627\u0644\u0630\u064a \u064a\u062d\u062f\u062b \u0641\u064a \u0627\u0644\u0645\u0642\u062f\u0631\u0627\u062a.<\/p>\n<p style=\"text-align: justify;\">3- \u0648\u0642\u062f \u0644\u0648\u062d\u0638\u060c \u0628\u063a\u0636 \u0627\u0644\u0646\u0638\u0631 \u0639\u0646 \u0627\u0644\u0632\u064a\u0627\u062f\u0629 \u0641\u064a \u062d\u062c\u0645 \u0627\u0644\u0639\u064a\u0646\u0629 n 80 ,70 ,60 =\u0623\u0648 \u0632\u064a\u0627\u062f\u0629 \u0645\u0639\u0627\u0645\u0644 \u0627\u0644\u0627\u0631\u062a\u0628\u0627\u0637 \u03c1\u060c \u0641\u064a \u062c\u0645\u064a\u0639 \u0627\u0644\u062d\u0627\u0644\u0627\u062a \u0639\u0646\u062f 20= p \u064850 \u0648100\u060c \u064a\u062d\u062a\u0641\u0638 \u0645\u0642\u062f\u0631 \u0627\u0646\u062d\u062f\u0627\u0631 \u0631\u064a\u062f\u062c Ridge \u0628\u0627\u0644\u0645\u0631\u0643\u0632 \u0627\u0644\u0623\u0648\u0644 \u0648\u064a\u062a\u0628\u0639\u0647 \u0641\u064a \u0627\u0644\u0645\u0631\u0643\u0632 \u0627\u0644\u062b\u0627\u0646\u064a \u0645\u0642\u062f\u0631 \u0627\u0644\u0634\u0628\u0643\u0629 \u0627\u0644\u0645\u0631\u0646\u0629 \u0627\u0644\u062a\u0643\u064a\u0641\u064a\u0629 .Adaptive Elastic Net<\/p>\n<p style=\"text-align: justify;\">4- \u0641\u064a \u062d\u064a\u0646 \u0623\u0646 \u0645\u0642\u062f\u0631\u0627\u062a \u0627\u062e\u062a\u064a\u0627\u0631 \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u0627\u0644\u062b\u0644\u0627\u062b\u0629 \u0627\u0644\u0623\u062e\u0631\u0649: LASSO\u060c \u0648Adaptive LASSO\u060c \u0648Elastic Net \u062a\u0624\u062f\u064a \u0623\u062f\u0627\u0621\u064b \u062c\u064a\u062f\u064b\u0627 \u0644\u0644\u063a\u0627\u064a\u0629 \u0641\u064a \u0625\u0632\u0627\u0644\u0629 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062e\u0637\u064a\u0629 \u0627\u0644\u0645\u062a\u0639\u062f\u062f\u0629 \u0648\u0645\u0634\u0643\u0644\u0629 \u062a\u0639\u062f\u062f \u0627\u0644\u0627\u0628\u0639\u0627\u062f\u060c \u0625\u0644\u0627 \u0623\u0646\u0647\u0627 \u062a\u062a\u0645\u062a\u0639 \u0628\u062f\u0642\u0629 \u062a\u0646\u0628\u0624 \u0623\u0642\u0644.<\/p>\n<p style=\"text-align: justify;\"><strong>2.4 \u0627\u0644\u0646\u0645\u0637 \u0627\u0644\u062b\u0627\u0646\u064a: \u062d\u062f \u0627\u0644\u062e\u0637\u0623 \u063a\u064a\u0631 \u0645\u0648\u0632\u0639 \u062a\u0648\u0632\u064a\u0639\u0627\u064b \u0637\u0628\u064a\u0639\u064a\u0627\u064b<\/strong><\/p>\n<p style=\"text-align: justify;\">\u0623\u0645\u0627 \u0641\u064a \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0627\u0644\u062b\u0627\u0646\u064a\u0629 \u0641\u0642\u062f \u0627\u0641\u062a\u0631\u0636 \u0623\u0646 \u0627\u0644\u0623\u062e\u0637\u0627\u0621 \u062a\u0648\u0632\u0639\u062a \u0648\u0641\u0642 \u062a\u0648\u0632\u064a\u0639 t \u062b\u0642\u064a\u0644 \u0627\u0644\u0630\u064a\u0644 (\u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u063a\u064a\u0631 \u0627\u0644\u0637\u0628\u064a\u0639\u064a). \u062a\u0645 \u0625\u062c\u0631\u0627\u0621 \u062c\u0645\u064a\u0639 \u0627\u0644\u0625\u0639\u062f\u0627\u062f\u0627\u062a \u0627\u0644\u0623\u062e\u0631\u0649 \u0643\u0645\u0627 \u0641\u064a \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0627\u0644\u0623\u0648\u0644\u0649. \u062a\u0645 \u0627\u0644\u062a\u0648\u0635\u0644 \u0625\u0644\u0649 \u0627\u0644\u0646\u0642\u0627\u0637 \u0627\u0644\u062b\u0644\u0627\u062b \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0627\u0644\u0645\u062b\u064a\u0631\u0629 \u0644\u0644\u0627\u0647\u062a\u0645\u0627\u0645:<\/p>\n<p style=\"text-align: justify;\">1- \u0627\u0633\u062a\u0645\u0631\u0627\u0631 \u0645\u0642\u062f\u0631 OLS \u0641\u064a \u0625\u0639\u0637\u0627\u0621 \u0642\u064a\u0645 MSE \u0643\u0628\u064a\u0631\u0629 \u062c\u062f\u064b\u0627 \u0628\u0633\u0628\u0628 \u0648\u062c\u0648\u062f \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062e\u0637\u064a\u0629 \u0627\u0644\u0645\u062a\u0639\u062f\u062f\u0629.<\/p>\n<p style=\"text-align: justify;\">2- \u0645\u0639 \u0632\u064a\u0627\u062f\u0629 \u062d\u062c\u0645 \u0627\u0644\u0639\u064a\u0646\u0629 n 80 ,70 ,60 =\u060c \u064a\u0644\u0627\u062d\u0638 \u0623\u0646 \u0627\u0644\u0645\u0642\u062f\u0631 \u0641\u064a \u0627\u0644\u0645\u0642\u0627\u0645 \u0627\u0644\u0623\u0648\u0644 \u0647\u0648 \u0645\u0642\u062f\u0631 \u0627\u0646\u062d\u062f\u0627\u0631 \u0631\u064a\u062f\u062c Ridge\u060c \u064a\u0644\u064a\u0647 \u0641\u064a \u0627\u0644\u0645\u0631\u0643\u0632 \u0627\u0644\u062b\u0627\u0646\u064a \u0645\u0642\u062f\u0631 Elastic net\u062b\u0645 \u0641\u064a \u0627\u0644\u0645\u0631\u0643\u0632 \u0627\u0644\u062b\u0627\u0644\u062b \u0645\u0642\u062f\u0631\u0627\u0646 \u0645\u062a\u0633\u0627\u0648\u064a\u0627\u0646 \u062a\u0642\u0631\u064a\u0628\u064b\u0627 \u0641\u064a \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u060c \u0648\u0647\u0645\u0627 \u0645\u0642\u062f\u0631 Adaptive Elastic Net \u0648 Lasso \u0648\u0647\u0630\u0627 \u0627\u0644\u0627\u062e\u064a\u0631 \u0645\u062d\u062a\u0645\u0644 \u0623\u064a\u0636\u064b\u0627 \u0641\u064a \u062d\u0627\u0644\u0629 \u0627\u0644\u0639\u064a\u0646\u0627\u062a \u0627\u0644\u0635\u063a\u064a\u0631\u0629 \u0639\u0646\u062f\u0645\u0627 \u0639\u062f\u062f \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a p= 20.<\/p>\n<p style=\"text-align: justify;\">3- \u0644\u0648\u062d\u0638 \u0623\u0646\u0647 \u0641\u064a \u062d\u0627\u0644\u0629 \u0627\u0644\u0646\u0645\u0637 \u0627\u0644\u062b\u0627\u0646\u064a\u060c \u0628\u063a\u0636 \u0627\u0644\u0646\u0638\u0631 \u0639\u0646 \u062d\u062c\u0645 \u0627\u0644\u0639\u064a\u0646\u0629 n 40 ,30 ,20 =\u0648\u0639\u062f\u062f \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a p=50\u060c \u0641\u0625\u0646 \u0645\u0642\u062f\u0631 \u0627\u0644\u0634\u0628\u0643\u0629 \u0627\u0644\u0645\u0631\u0646\u0629 \u0627\u0644\u062a\u0643\u064a\u0641\u064a\u0629 Adaptive Elastic Net \u064a\u0639\u0645\u0644 \u0628\u0634\u0643\u0644 \u0623\u0641\u0636\u0644 \u0648\u0647\u0648 \u064a\u0623\u062a\u064a \u0628\u0639\u062f \u0630\u0644\u0643 \u0645\u0642\u062f\u0631 \u0627\u0646\u062d\u062f\u0627\u0631 \u0631\u064a\u062f\u062c Ridge.<\/p>\n<p style=\"text-align: justify;\">\u0644\u0645\u0642\u0627\u0631\u0646\u0629 \u062a\u0623\u062b\u064a\u0631 \u062a\u0628\u0639\u064a\u0629 \u062d\u062f \u0627\u0644\u062e\u0637\u0623 \u0627\u0644\u064a \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a \u0627\u0644\u0646\u0627\u062a\u062c\u0629 \u0639\u0646 \u0627\u0644\u062a\u063a\u064a\u064a\u0631 \u0645\u0646 \u0627\u0644\u0646\u0645\u0637 1 \u0625\u0644\u0649 \u0627\u0644\u0646\u0645\u0637 2:<\/p>\n<p style=\"text-align: justify;\">1- \u0648\u064a\u0644\u0627\u062d\u0638 \u0628\u063a\u0636 \u0627\u0644\u0646\u0638\u0631 \u0639\u0646 \u0646\u0648\u0639 \u062a\u0648\u0632\u064a\u0639 \u062d\u062f \u0627\u0644\u062e\u0637\u0623\u060c \u0641\u0625\u0630\u0627 \u0643\u0627\u0646 \u0639\u062f\u062f \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u064a\u0633\u0627\u0648\u064a p=20,50,100\u060c \u0647\u0646\u0627\u0643 \u0627\u062a\u0641\u0627\u0642 \u062d\u0648\u0644 \u0627\u0644\u0645\u0642\u062f\u0631 \u0627\u0644\u0630\u064a \u064a\u062d\u062a\u0644 \u0627\u0644\u0645\u0631\u0643\u0632 \u0627\u0644\u0623\u0648\u0644 \u0648\u0647\u0648 \u0645\u0642\u062f\u0631 \u0627\u0646\u062d\u062f\u0627\u0631 \u0631\u064a\u062f\u062c Ridge. \u0628\u064a\u0646\u0645\u0627 \u0627\u0644\u0645\u0631\u0643\u0632 \u0627\u0644\u062b\u0627\u0646\u064a \u064a\u0643\u0648\u0646 \u0644\u0645\u0642\u062f\u0631 \u0627\u0644\u0634\u0628\u0643\u0629 \u0627\u0644\u0645\u0631\u0646\u0629 \u0627\u0644\u062a\u0643\u064a\u0641\u064a\u0629 Adaptive Elastic Net \u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u0647\u0646\u0627\u0643 \u0627\u062e\u062a\u0644\u0627\u0641 \u0641\u064a \u0627\u0644\u0645\u0642\u062f\u0631 \u0627\u0644\u0630\u064a \u064a\u062d\u062a\u0644 \u0627\u0644\u0645\u0631\u0643\u0632 \u0627\u0644\u062b\u0627\u0644\u062b\u060c \u062d\u064a\u062b \u064a\u0644\u0627\u062d\u0638 \u0623\u0646\u0647 \u064a\u062a\u0623\u0631\u062c\u062d \u0628\u064a\u0646 \u0627\u0644\u0645\u0642\u062f\u0631 Lasso \u0648\u0627\u0644\u0645\u0642\u062f\u0631 Elastic net \u0639\u0646\u062f \u0628\u0639\u0636 \u0627\u0644\u0642\u064a\u0645.<\/p>\n<p style=\"text-align: justify;\">\u2022 \u0623\u062b\u0628\u062a \u0627\u0644\u062e\u0645\u0633\u0629 \u0645\u0642\u062f\u0631\u0627\u062a \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062c\u0632\u0627\u0626\u064a\u0629 \u0645\u062e\u062a\u0644\u0641\u0629 \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645\u0629 \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062f\u0631\u0627\u0633\u0629 \u0642\u0648\u0629 \u0645\u0631\u0648\u0646\u062a\u0647\u0627 (Robustness) \u062a\u062c\u0627\u0647 \u062a\u0628\u0639\u064a\u0629 \u062d\u062f \u0627\u0644\u062e\u0637\u0623 \u0627\u0644\u064a \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a\u060c \u062d\u064a\u062b \u0644\u0645 \u064a\u0643\u0646 \u0647\u0646\u0627\u0643 \u062a\u0623\u062b\u064a\u0631 \u0643\u0628\u064a\u0631 \u0639\u0644\u0649 \u0646\u062a\u0627\u0626\u062c \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629.<\/p>\n<p style=\"text-align: justify;\">\u0643\u062a\u0639\u0644\u064a\u0642 \u0623\u062e\u064a\u0631\u060c \u0623\u0638\u0647\u0631\u062a \u0627\u0644\u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0627\u0644\u062a\u064a \u0623\u062c\u0631\u064a\u062a \u0639\u0644\u0649 \u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0623\u0646 \u0642\u064a\u0645 MSE \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0642\u062f\u0631 \u0627\u0646\u062d\u062f\u0627\u0631 \u0631\u064a\u062f\u062c Ridge \u062a\u0645\u064a\u0644 \u0625\u0644\u0649 \u062a\u0642\u0644\u064a\u0644 \u0639\u062f\u062f \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u0645\u062d\u062f\u062f\u0629 \u0628\u0634\u0643\u0644 \u0643\u0628\u064a\u0631\u060c \u0645\u0639 \u0627\u0644\u062d\u0641\u0627\u0638 \u0639\u0644\u0649 \u062f\u0642\u0629 \u0627\u0644\u062a\u0642\u062f\u064a\u0631\u060c \u0648\u0647\u064a \u062e\u0627\u0635\u064a\u0629 \u0645\u0631\u063a\u0648\u0628\u0629 \u0641\u064a \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0645\u0634\u0643\u0644\u0627\u062a \u0627\u062e\u062a\u064a\u0627\u0631 \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u0648\u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u062a\u062d\u064a\u0632 \u0641\u064a \u0627\u0644\u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629 \u0641\u064a \u0627\u0644\u0639\u0627\u0644\u0645 \u0627\u0644\u062d\u0642\u064a\u0642\u064a.<\/p>\n<p style=\"text-align: justify;\">\u0644\u0630\u0644\u0643\u060c \u064a\u062d\u0627\u0641\u0638 \u0645\u0642\u062f\u0631 \u0627\u0646\u062d\u062f\u0627\u0631 \u0631\u064a\u062f\u062c Ridge \u0639\u0644\u0649 \u062a\u0641\u0648\u0642\u0647 \u0639\u0644\u0649 \u062c\u0645\u064a\u0639 \u0627\u0644\u0645\u0642\u062f\u0631\u0627\u062a \u0627\u0644\u0623\u062e\u0631\u0649\u060c \u0644\u0623\u0646\u0647 \u064a\u0639\u0637\u064a \u0623\u0635\u063a\u0631 \u0642\u064a\u0645\u0629 MSE \u0648\u0643\u0630\u0644\u0643 \u0623\u0635\u063a\u0631 \u0642\u064a\u0645\u0629 \u0644\u0644\u0627\u0646\u062d\u0631\u0627\u0641 \u0627\u0644\u0645\u0639\u064a\u0627\u0631\u064a \u0628\u063a\u0636 \u0627\u0644\u0646\u0638\u0631 \u0644\u0627\u062e\u062a\u0644\u0627\u0641 \u0645\u0639\u0627\u0645\u0644 \u0627\u0644\u0627\u0631\u062a\u0628\u0627\u0637 \u03c1 \u0627\u0648 \u0639\u062f\u062f \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u062a\u0648\u0636\u064a\u062d\u064a\u0629 p \u0627\u0648 \u062d\u062c\u0645 \u0627\u0644\u0639\u064a\u0646\u0629 n. \u0643\u0645\u0627 \u064a\u062d\u0627\u0641\u0638 \u0645\u0642\u062f\u0631 Elastic net\u0639\u0644\u0649 \u0627\u0644\u0645\u0631\u0643\u0632 \u0627\u0644\u062b\u0627\u0646\u064a.<\/p>\n<p style=\"text-align: justify;\">\u062a\u0639\u062a\u0628\u0631 \u0642\u064a\u0645\u0629 MSE \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0642\u062f\u0631 Adaptive Elastic Net \u0623\u0643\u062b\u0631 \u0623\u0645\u0627\u0646\u064b\u0627 \u0645\u0646 LASSO \u0648Adaptive LASSO\u060c \u0645\u0646 \u062e\u0644\u0627\u0644 \u062a\u0642\u062f\u064a\u0645 \u062a\u0646\u0638\u064a\u0645 L<sub>2<\/sub>\u060c \u0645\u0645\u0627 \u0642\u062f \u064a\u0624\u062f\u064a \u0625\u0644\u0649 \u062a\u062c\u0646\u0628 \u0627\u0644\u062d\u0630\u0641 \u0627\u0644\u0645\u062a\u0647\u0648\u0631 \u0644\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u0645\u0647\u0645\u0629 \u0627\u0644\u0645\u0631\u062a\u0628\u0637\u0629\u060c \u0645\u0639 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0623\u0642\u0644 \u062a\u062d\u062f\u064a\u062f\u064b\u0627 \u0628\u0643\u062b\u064a\u0631 \u0645\u0646 \u0645\u0642\u062f\u0631 \u0627\u0644\u0634\u0628\u0643\u0629 \u0627\u0644\u0645\u0631\u0646\u0629 \u0627\u0644\u062a\u0643\u064a\u0641\u064a\u0629 . Adaptive Elastic Net<\/p>\n<p style=\"text-align: justify;\">\u0631\u0628\u0645\u0627 \u062a\u0643\u0648\u0646 \u0647\u0630\u0647 \u0647\u064a \u0627\u0644\u0645\u0641\u0627\u0636\u0644\u0629 \u0636\u0645\u0646 \u0642\u064a\u0645\u0629 MSE \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0642\u062f\u0631 Adaptive Elastic Net \u0648Adaptive LASSO \u0641\u064a \u062f\u0642\u0629 \u0627\u0644\u062a\u0646\u0628\u0624\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u062a\u0648\u0641\u0631 \u0644\u0646\u0627 \u0631\u0624\u064a\u0629 \u0623\u0643\u062b\u0631 \u062d\u0648\u0644 \u0645\u0648\u0627\u0635\u0644\u0629 \u0641\u062d\u0635 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0642\u0644\u0629 \u0627\u0644\u0645\u0631\u062a\u0628\u0637\u0629. \u0639\u0644\u0627\u0648\u0629 \u0639\u0644\u0649 \u0630\u0644\u0643\u060c \u062a\u062c\u062f\u0631 \u0627\u0644\u0625\u0634\u0627\u0631\u0629 \u0625\u0644\u0649 \u0623\u0646\u0647 \u0645\u0646 \u062e\u0644\u0627\u0644 \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0630\u0641\u0647\u0627 \u0641\u064a \u0643\u0644 \u062e\u0637\u0648\u0629\u060c \u064a\u0645\u0643\u0646 \u0627\u0643\u062a\u0633\u0627\u0628 \u0627\u0644\u0645\u0632\u064a\u062f \u0645\u0646 \u0627\u0644\u0645\u0639\u0631\u0641\u0629 \u062d\u0648\u0644 \u0628\u0646\u064a\u0629 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0642\u0644\u0629 \u0627\u0644\u0645\u0631\u062a\u0628\u0637\u0629.<\/p>\n<p style=\"text-align: justify;\">\u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u0645\u0646\u0627\u0642\u0634\u0629\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0623\u0646 \u0646\u0631\u0649 \u0623\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0642\u062f\u0631\u0627\u062a Adaptive LASSO \u0648Elastic Net \u064a\u0639\u062f \u0623\u0645\u0631\u064b\u0627 \u0639\u0645\u0644\u064a\u064b\u0627 \u062a\u0645\u0627\u0645\u064b\u0627 \u0641\u064a \u0627\u0644\u0638\u0631\u0648\u0641 \u0627\u0644\u062a\u064a \u064a\u064f\u0639\u062a\u0642\u062f \u0641\u064a\u0647\u0627 \u0623\u0646 \u0642\u064a\u0645 \u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0646\u0645\u0648\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0643\u0628\u064a\u0631\u0629 \u063a\u064a\u0631 \u0645\u062d\u062a\u0645\u0644\u0629 \u0645\u0646 \u0648\u062c\u0647\u0629 \u0646\u0638\u0631 \u0639\u0645\u0644\u064a\u0629.<\/p>\n<p style=\"text-align: justify;\">\u0648\u062e\u062a\u0627\u0645\u0627\u060c \u064a\u0648\u0635\u0649 \u0628\u0634\u062f\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0642\u062f\u0631\u0627\u062a \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062c\u0632\u0627\u0626\u064a\u0629 \u0644\u062d\u0644 \u0645\u0634\u0643\u0644\u0627\u062a \u0645\u0644\u0627\u0621\u0645\u0629 \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u0627\u0644\u062a\u064a \u062a\u062a\u0636\u0645\u0646 \u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0639\u062f\u062f \u0627\u0644\u062e\u0637\u064a \u0648\u062a\u0639\u062f\u062f \u0627\u0644\u0627\u0628\u0639\u0627\u062f\u060c \u0646\u0638\u0631\u064b\u0627 \u0644\u0648\u062c\u0648\u062f \u0623\u062f\u0644\u0629 \u0625\u064a\u062c\u0627\u0628\u064a\u0629 \u0643\u0627\u0641\u064a\u0629 \u062d\u0648\u0644 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u062a\u062d\u064a\u0632 \u062a\u0634\u064a\u0631 \u0625\u0644\u0649 \u0623\u0646\u0647 \u064a\u062c\u0628 \u0623\u0646 \u064a\u0643\u0648\u0646 \u062c\u0632\u0621\u064b\u0627 \u0645\u0646 \u0623\u064a \u062a\u0642\u0646\u064a\u0629 \u0644\u0627\u062e\u062a\u064a\u0627\u0631 \u0627\u0644\u0646\u0645\u0648\u0630\u062c.<\/p>\n<p style=\"text-align: justify;\"><strong>\u0627\u0644\u0645\u0631\u0627\u062c\u0639 \u0648\u0627\u0644\u0645\u0635\u0627\u062f\u0631<\/strong><\/p>\n<ol style=\"text-align: justify;\">\n<li dir=\"ltr\"><a href=\"https:\/\/onlinelibrary.wiley.com\/authored-by\/\">Agresti<\/a>, Alan (2002) Categorical Data Analysis, John Wiley and Sons, USA.<\/li>\n<li dir=\"ltr\">Baltagi, B. H. (2001). &#8220;<em>Econometric Analysis of Panel Data&#8221;<\/em>. Wiley, John &amp; Sons:New York .<\/li>\n<li dir=\"ltr\">Bates, D.M. and Watts, D.G (1988). Nonlinear Regression Analysis<\/li>\n<\/ol>\n<p dir=\"ltr\" style=\"text-align: justify;\">and Its Applications<em>.<\/em> John Wiley and Sons, USA.<\/p>\n<ol dir=\"ltr\">\n<li style=\"text-align: justify;\">Galton, Francis (1886) &#8220;<em>Regression towards mediocrity in hereditary stature<\/em>.&#8221;\u00a0The Journal of the Anthropological Institute of Great Britain and Ireland\u00a0vol.<strong> 15<\/strong>: pp. 246-263.<\/li>\n<li style=\"text-align: justify;\">Greene, W. H. (2000). Econometric Analysis, 4th Edition. Prentice.<\/li>\n<li style=\"text-align: justify;\">Hastie, T., Tibshirani, R., and Friedman, J. (2002). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer-Verlag, New York, NY: USA.<\/li>\n<li style=\"text-align: justify;\">Helwig, N. E. (2017). \u201c<em>Adding bias to reduce variance in psychology results: A tutorial on Penalized regression<\/em>\u201d. The Quantitive Methods for Psychology, vol. 13(1) pp. 1-19.<\/li>\n<li style=\"text-align: justify;\">Hocking, R. R., Speed, F. M., and Lynn M. J. (1976) \u201c<em>A Class of Biased Estimators in Linear Regression\u201d<\/em>, Technometrics vol. 18, No. 4, pp. 425-437<\/li>\n<li style=\"text-align: justify;\">Hoerl A.E., and Kennard R.W. (1975) \u201c<em>Ridge regression: Biased estimation for nonorthogonal problems\u201d<\/em>. Technometrics. Vol. 12: pp 55\u201367.<\/li>\n<li style=\"text-align: justify;\"><a href=\"https:\/\/typeset.io\/authors\/donald-w-marquaridt-2mbz7annp2\">Marquaridt<\/a>, Donald W. 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