{"id":702,"date":"2018-01-27T14:36:31","date_gmt":"2018-01-27T14:36:31","guid":{"rendered":"http:\/\/jsr.isrt.ac.bd\/?post_type=article&#038;p=702"},"modified":"2018-01-27T14:36:46","modified_gmt":"2018-01-27T14:36:46","slug":"shrinkage-selection-anova-model","status":"publish","type":"article","link":"http:\/\/jsr.isrt.ac.bd\/article\/shrinkage-selection-anova-model\/","title":{"rendered":"On shrinkage and selection: ANOVA model"},"content":{"rendered":"<p>This paper considers the estimation of the parameters of an ANOVA model<br \/>\nwhen sparsity is suspected. Accordingly, we consider the least square estima-<br \/>\ntor (LSE), restricted LSE, preliminary test and Stein-type estimators, together<br \/>\nwith three penalty estimators, namely, the ridge estimator, subset selection rules<br \/>\n(hard threshold estimator) and the LASSO (soft threshold estimator). We com-<br \/>\npare and contrast the L2-risk of all the estimators with the lower bound of L2-<br \/>\nrisk of LASSO in a family of diagonal projection scheme which is also the lower<br \/>\nbound of the exact L2-risk of LASSO. The result of this comparison is that nei-<br \/>\nther LASSO nor the LSE, preliminary test, and Stein-type estimators outperform<br \/>\neach other uniformly. However, when the model is sparse, LASSO outperforms<br \/>\nall estimators except &#8220;ridge&#8221; estimator since both LASSO and ridge are L2-risk<br \/>\nequivalent under sparsity. We also \fnd that LASSO and the restricted LSE are<br \/>\nL2-risk equivalent and both outperform all estimators (except ridge) depending<br \/>\non the dimension of sparsity. Finally, ridge estimator outperforms all estimators<br \/>\nuniformly. Our \fnding are based on L2-risk of estimators and lower bound of the<br \/>\nrisk of LASSO together with tables of efficiency and graphical display of efficiency<br \/>\nand not based on simulation.<\/p>\n<p><a href=\"http:\/\/jsr.isrt.ac.bd\/wp-content\/uploads\/51n2_5.pdf\">51n2_5<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This paper considers the estimation of the parameters of an ANOVA model when sparsity is suspected. Accordingly, we consider the least square estima- tor (LSE), restricted LSE, preliminary test and Stein-type estimators, together with three penalty estimators, namely, the ridge estimator, subset selection rules (hard threshold estimator) and the LASSO (soft threshold estimator). We com- [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","format":"standard","meta":{"_mi_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"issuem_issue":[22],"issuem_issue_categories":[],"issuem_issue_tags":[],"class_list":["post-702","article","type-article","status-publish","format-standard","hentry","issuem_issue-v51n2"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v22.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>On shrinkage and selection: ANOVA model - JSR<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/jsr.isrt.ac.bd\/article\/shrinkage-selection-anova-model\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"On shrinkage and selection: ANOVA model - JSR\" \/>\n<meta property=\"og:description\" content=\"This paper considers the estimation of the parameters of an ANOVA model when sparsity is suspected. Accordingly, we consider the least square estima- tor (LSE), restricted LSE, preliminary test and Stein-type estimators, together with three penalty estimators, namely, the ridge estimator, subset selection rules (hard threshold estimator) and the LASSO (soft threshold estimator). We com- [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/jsr.isrt.ac.bd\/article\/shrinkage-selection-anova-model\/\" \/>\n<meta property=\"og:site_name\" content=\"JSR\" \/>\n<meta property=\"article:modified_time\" content=\"2018-01-27T14:36:46+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/jsr.isrt.ac.bd\/article\/shrinkage-selection-anova-model\/\",\"url\":\"https:\/\/jsr.isrt.ac.bd\/article\/shrinkage-selection-anova-model\/\",\"name\":\"On shrinkage and selection: ANOVA model - JSR\",\"isPartOf\":{\"@id\":\"https:\/\/jsr.isrt.ac.bd\/#website\"},\"datePublished\":\"2018-01-27T14:36:31+00:00\",\"dateModified\":\"2018-01-27T14:36:46+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/jsr.isrt.ac.bd\/article\/shrinkage-selection-anova-model\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/jsr.isrt.ac.bd\/article\/shrinkage-selection-anova-model\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/jsr.isrt.ac.bd\/article\/shrinkage-selection-anova-model\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/jsr.isrt.ac.bd\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Articles\",\"item\":\"https:\/\/jsr.isrt.ac.bd\/article\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"On shrinkage and selection: ANOVA model\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/jsr.isrt.ac.bd\/#website\",\"url\":\"https:\/\/jsr.isrt.ac.bd\/\",\"name\":\"JSR\",\"description\":\"Journal of Statistical Research\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/jsr.isrt.ac.bd\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"On shrinkage and selection: ANOVA model - JSR","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/jsr.isrt.ac.bd\/article\/shrinkage-selection-anova-model\/","og_locale":"en_US","og_type":"article","og_title":"On shrinkage and selection: ANOVA model - JSR","og_description":"This paper considers the estimation of the parameters of an ANOVA model when sparsity is suspected. Accordingly, we consider the least square estima- tor (LSE), restricted LSE, preliminary test and Stein-type estimators, together with three penalty estimators, namely, the ridge estimator, subset selection rules (hard threshold estimator) and the LASSO (soft threshold estimator). We com- [&hellip;]","og_url":"https:\/\/jsr.isrt.ac.bd\/article\/shrinkage-selection-anova-model\/","og_site_name":"JSR","article_modified_time":"2018-01-27T14:36:46+00:00","twitter_card":"summary_large_image","twitter_misc":{"Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/jsr.isrt.ac.bd\/article\/shrinkage-selection-anova-model\/","url":"https:\/\/jsr.isrt.ac.bd\/article\/shrinkage-selection-anova-model\/","name":"On shrinkage and selection: ANOVA model - JSR","isPartOf":{"@id":"https:\/\/jsr.isrt.ac.bd\/#website"},"datePublished":"2018-01-27T14:36:31+00:00","dateModified":"2018-01-27T14:36:46+00:00","breadcrumb":{"@id":"https:\/\/jsr.isrt.ac.bd\/article\/shrinkage-selection-anova-model\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/jsr.isrt.ac.bd\/article\/shrinkage-selection-anova-model\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/jsr.isrt.ac.bd\/article\/shrinkage-selection-anova-model\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/jsr.isrt.ac.bd\/"},{"@type":"ListItem","position":2,"name":"Articles","item":"https:\/\/jsr.isrt.ac.bd\/article\/"},{"@type":"ListItem","position":3,"name":"On shrinkage and selection: ANOVA model"}]},{"@type":"WebSite","@id":"https:\/\/jsr.isrt.ac.bd\/#website","url":"https:\/\/jsr.isrt.ac.bd\/","name":"JSR","description":"Journal of Statistical Research","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/jsr.isrt.ac.bd\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"}]}},"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/article\/702","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/article"}],"about":[{"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/types\/article"}],"author":[{"embeddable":true,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/comments?post=702"}],"version-history":[{"count":0,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/article\/702\/revisions"}],"wp:attachment":[{"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/media?parent=702"}],"wp:term":[{"taxonomy":"issuem_issue","embeddable":true,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/issuem_issue?post=702"},{"taxonomy":"issuem_issue_categories","embeddable":true,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/issuem_issue_categories?post=702"},{"taxonomy":"issuem_issue_tags","embeddable":true,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/issuem_issue_tags?post=702"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}