{"id":660,"date":"2017-09-28T08:29:32","date_gmt":"2017-09-28T08:29:32","guid":{"rendered":"http:\/\/jsr.isrt.ac.bd\/?post_type=article&#038;p=660"},"modified":"2017-09-28T08:30:18","modified_gmt":"2017-09-28T08:30:18","slug":"estimation-parameters-simple-multivariate-linear-model-student-t-errors","status":"publish","type":"article","link":"http:\/\/jsr.isrt.ac.bd\/article\/estimation-parameters-simple-multivariate-linear-model-student-t-errors\/","title":{"rendered":"Estimation of parameters of the simple multivariate linear model with student t-errors"},"content":{"rendered":"<p>This paper considers estimation of the intercept and slope vector parameters of<br \/>\nthe simple multivariate linear regression model with Student-t errors in the presence<br \/>\nof uncertain prior information on the value of the unknown slope vector. The<br \/>\nunrestricted, restricted, preliminary test, shrinkage, and positive-rule shrinkage<br \/>\nestimators are defined together with the expressions for the bias, quadratic bias,<br \/>\nquadratic risk and mean squared errors (mse) functions of the estimators are derived.<br \/>\nComparison of the estimators is made using quadratic risk criterion. Based<br \/>\non the study we conclude that for <img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/jsr.isrt.ac.bd\/wp-content\/ql-cache\/quicklatex.com-4f2ccd992442a4a996dab72128be4192_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#32;&#103;&#101;&#113;&#32;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"45\" style=\"vertical-align: -4px;\"\/> shrinkage estimators are recommended,<br \/>\nand for <img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/jsr.isrt.ac.bd\/wp-content\/ql-cache\/quicklatex.com-80459010e3b8da3fc98c6597dd6f125a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#92;&#108;&#101;&#113;&#32;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\"\/>, the preliminary test estimators are preferable.<\/p>\n<p><a href=\"http:\/\/jsr.isrt.ac.bd\/wp-content\/uploads\/39n2_5.pdf\">Fulltext<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This paper considers estimation of the intercept and slope vector parameters of the simple multivariate linear regression model with Student-t errors in the presence of uncertain prior information on the value of the unknown slope vector. The unrestricted, restricted, preliminary test, shrinkage, and positive-rule shrinkage estimators are defined together with the expressions for the bias, [&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":[21],"issuem_issue_categories":[],"issuem_issue_tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v22.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Estimation of parameters of the simple multivariate linear model with student t-errors - 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\/estimation-parameters-simple-multivariate-linear-model-student-t-errors\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Estimation of parameters of the simple multivariate linear model with student t-errors - JSR\" \/>\n<meta property=\"og:description\" content=\"This paper considers estimation of the intercept and slope vector parameters of the simple multivariate linear regression model with Student-t errors in the presence of uncertain prior information on the value of the unknown slope vector. The unrestricted, restricted, preliminary test, shrinkage, and positive-rule shrinkage estimators are defined together with the expressions for the bias, [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/jsr.isrt.ac.bd\/article\/estimation-parameters-simple-multivariate-linear-model-student-t-errors\/\" \/>\n<meta property=\"og:site_name\" content=\"JSR\" \/>\n<meta property=\"article:modified_time\" content=\"2017-09-28T08:30:18+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\/estimation-parameters-simple-multivariate-linear-model-student-t-errors\/\",\"url\":\"https:\/\/jsr.isrt.ac.bd\/article\/estimation-parameters-simple-multivariate-linear-model-student-t-errors\/\",\"name\":\"Estimation of parameters of the simple multivariate linear model with student t-errors - JSR\",\"isPartOf\":{\"@id\":\"https:\/\/jsr.isrt.ac.bd\/#website\"},\"datePublished\":\"2017-09-28T08:29:32+00:00\",\"dateModified\":\"2017-09-28T08:30:18+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/jsr.isrt.ac.bd\/article\/estimation-parameters-simple-multivariate-linear-model-student-t-errors\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/jsr.isrt.ac.bd\/article\/estimation-parameters-simple-multivariate-linear-model-student-t-errors\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/jsr.isrt.ac.bd\/article\/estimation-parameters-simple-multivariate-linear-model-student-t-errors\/#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\":\"Estimation of parameters of the simple multivariate linear model with student t-errors\"}]},{\"@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":"Estimation of parameters of the simple multivariate linear model with student t-errors - 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\/estimation-parameters-simple-multivariate-linear-model-student-t-errors\/","og_locale":"en_US","og_type":"article","og_title":"Estimation of parameters of the simple multivariate linear model with student t-errors - JSR","og_description":"This paper considers estimation of the intercept and slope vector parameters of the simple multivariate linear regression model with Student-t errors in the presence of uncertain prior information on the value of the unknown slope vector. The unrestricted, restricted, preliminary test, shrinkage, and positive-rule shrinkage estimators are defined together with the expressions for the bias, [&hellip;]","og_url":"https:\/\/jsr.isrt.ac.bd\/article\/estimation-parameters-simple-multivariate-linear-model-student-t-errors\/","og_site_name":"JSR","article_modified_time":"2017-09-28T08:30:18+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\/estimation-parameters-simple-multivariate-linear-model-student-t-errors\/","url":"https:\/\/jsr.isrt.ac.bd\/article\/estimation-parameters-simple-multivariate-linear-model-student-t-errors\/","name":"Estimation of parameters of the simple multivariate linear model with student t-errors - JSR","isPartOf":{"@id":"https:\/\/jsr.isrt.ac.bd\/#website"},"datePublished":"2017-09-28T08:29:32+00:00","dateModified":"2017-09-28T08:30:18+00:00","breadcrumb":{"@id":"https:\/\/jsr.isrt.ac.bd\/article\/estimation-parameters-simple-multivariate-linear-model-student-t-errors\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/jsr.isrt.ac.bd\/article\/estimation-parameters-simple-multivariate-linear-model-student-t-errors\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/jsr.isrt.ac.bd\/article\/estimation-parameters-simple-multivariate-linear-model-student-t-errors\/#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":"Estimation of parameters of the simple multivariate linear model with student t-errors"}]},{"@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\/660"}],"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=660"}],"version-history":[{"count":0,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/article\/660\/revisions"}],"wp:attachment":[{"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/media?parent=660"}],"wp:term":[{"taxonomy":"issuem_issue","embeddable":true,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/issuem_issue?post=660"},{"taxonomy":"issuem_issue_categories","embeddable":true,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/issuem_issue_categories?post=660"},{"taxonomy":"issuem_issue_tags","embeddable":true,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/issuem_issue_tags?post=660"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}