{"id":634,"date":"2017-09-28T06:50:45","date_gmt":"2017-09-28T06:50:45","guid":{"rendered":"http:\/\/jsr.isrt.ac.bd\/?post_type=article&#038;p=634"},"modified":"2017-09-28T06:50:53","modified_gmt":"2017-09-28T06:50:53","slug":"predictive-distribution-heteroscedastic-multivariate-linear-models-elliptically-contoured-error-distributions","status":"publish","type":"article","link":"http:\/\/jsr.isrt.ac.bd\/article\/predictive-distribution-heteroscedastic-multivariate-linear-models-elliptically-contoured-error-distributions\/","title":{"rendered":"The predictive distribution for the heteroscedastic multivariate linear models with elliptically contoured error distributions"},"content":{"rendered":"<p>This paper considers the heteroscedastic multivariate linear model with errors<br \/>\nfollowing elliptically contoured distributions. The marginal likelihood function of<br \/>\nthe unknown covariance parameters and the predictive distribution of future responses<br \/>\nhave been derived. The predictive distribution obtained is a product of m<br \/>\nmultivariate Student\u2019s t distributions. It is interesting to note that when the models<br \/>\nare assumed to have elliptically contoured distributions the marginal likelihood<br \/>\nfunction of the parameters as well as the predictive distribution are identical to<br \/>\nthose obtained under independently distributed normal errors or dependent but<br \/>\nuncorrelated Student\u2019s <img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/jsr.isrt.ac.bd\/wp-content\/ql-cache\/quicklatex.com-6b97bb0f65c75b6cc0fba1868749478d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"\/> errors. Therefore, the distribution of future responses<br \/>\nis unaffected by a change in the error distribution from the multivariate normal<br \/>\nand multivariate t distributions to elliptically contoured distributions. This gives<br \/>\ninference robustness with respect to departure from the reference case of independent<br \/>\nsampling from the multivariate normal or dependent but uncorrelated<br \/>\nsampling from multivariate t distributions to elliptically contoured distributions.<\/p>\n<p><a href=\"http:\/\/jsr.isrt.ac.bd\/wp-content\/uploads\/40n1_3.pdf\">Fulltext<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This paper considers the heteroscedastic multivariate linear model with errors following elliptically contoured distributions. The marginal likelihood function of the unknown covariance parameters and the predictive distribution of future responses have been derived. The predictive distribution obtained is a product of m multivariate Student\u2019s t distributions. It is interesting to note that when the models [&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":[20],"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>The predictive distribution for the heteroscedastic multivariate linear models with elliptically contoured error distributions - 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\/predictive-distribution-heteroscedastic-multivariate-linear-models-elliptically-contoured-error-distributions\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The predictive distribution for the heteroscedastic multivariate linear models with elliptically contoured error distributions - JSR\" \/>\n<meta property=\"og:description\" content=\"This paper considers the heteroscedastic multivariate linear model with errors following elliptically contoured distributions. The marginal likelihood function of the unknown covariance parameters and the predictive distribution of future responses have been derived. The predictive distribution obtained is a product of m multivariate Student\u2019s t distributions. It is interesting to note that when the models [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/jsr.isrt.ac.bd\/article\/predictive-distribution-heteroscedastic-multivariate-linear-models-elliptically-contoured-error-distributions\/\" \/>\n<meta property=\"og:site_name\" content=\"JSR\" \/>\n<meta property=\"article:modified_time\" content=\"2017-09-28T06:50:53+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\/predictive-distribution-heteroscedastic-multivariate-linear-models-elliptically-contoured-error-distributions\/\",\"url\":\"https:\/\/jsr.isrt.ac.bd\/article\/predictive-distribution-heteroscedastic-multivariate-linear-models-elliptically-contoured-error-distributions\/\",\"name\":\"The predictive distribution for the heteroscedastic multivariate linear models with elliptically contoured error distributions - JSR\",\"isPartOf\":{\"@id\":\"https:\/\/jsr.isrt.ac.bd\/#website\"},\"datePublished\":\"2017-09-28T06:50:45+00:00\",\"dateModified\":\"2017-09-28T06:50:53+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/jsr.isrt.ac.bd\/article\/predictive-distribution-heteroscedastic-multivariate-linear-models-elliptically-contoured-error-distributions\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/jsr.isrt.ac.bd\/article\/predictive-distribution-heteroscedastic-multivariate-linear-models-elliptically-contoured-error-distributions\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/jsr.isrt.ac.bd\/article\/predictive-distribution-heteroscedastic-multivariate-linear-models-elliptically-contoured-error-distributions\/#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\":\"The predictive distribution for the heteroscedastic multivariate linear models with elliptically contoured error distributions\"}]},{\"@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":"The predictive distribution for the heteroscedastic multivariate linear models with elliptically contoured error distributions - 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\/predictive-distribution-heteroscedastic-multivariate-linear-models-elliptically-contoured-error-distributions\/","og_locale":"en_US","og_type":"article","og_title":"The predictive distribution for the heteroscedastic multivariate linear models with elliptically contoured error distributions - JSR","og_description":"This paper considers the heteroscedastic multivariate linear model with errors following elliptically contoured distributions. The marginal likelihood function of the unknown covariance parameters and the predictive distribution of future responses have been derived. The predictive distribution obtained is a product of m multivariate Student\u2019s t distributions. It is interesting to note that when the models [&hellip;]","og_url":"https:\/\/jsr.isrt.ac.bd\/article\/predictive-distribution-heteroscedastic-multivariate-linear-models-elliptically-contoured-error-distributions\/","og_site_name":"JSR","article_modified_time":"2017-09-28T06:50:53+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\/predictive-distribution-heteroscedastic-multivariate-linear-models-elliptically-contoured-error-distributions\/","url":"https:\/\/jsr.isrt.ac.bd\/article\/predictive-distribution-heteroscedastic-multivariate-linear-models-elliptically-contoured-error-distributions\/","name":"The predictive distribution for the heteroscedastic multivariate linear models with elliptically contoured error distributions - JSR","isPartOf":{"@id":"https:\/\/jsr.isrt.ac.bd\/#website"},"datePublished":"2017-09-28T06:50:45+00:00","dateModified":"2017-09-28T06:50:53+00:00","breadcrumb":{"@id":"https:\/\/jsr.isrt.ac.bd\/article\/predictive-distribution-heteroscedastic-multivariate-linear-models-elliptically-contoured-error-distributions\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/jsr.isrt.ac.bd\/article\/predictive-distribution-heteroscedastic-multivariate-linear-models-elliptically-contoured-error-distributions\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/jsr.isrt.ac.bd\/article\/predictive-distribution-heteroscedastic-multivariate-linear-models-elliptically-contoured-error-distributions\/#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":"The predictive distribution for the heteroscedastic multivariate linear models with elliptically contoured error distributions"}]},{"@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\/634"}],"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=634"}],"version-history":[{"count":0,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/article\/634\/revisions"}],"wp:attachment":[{"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/media?parent=634"}],"wp:term":[{"taxonomy":"issuem_issue","embeddable":true,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/issuem_issue?post=634"},{"taxonomy":"issuem_issue_categories","embeddable":true,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/issuem_issue_categories?post=634"},{"taxonomy":"issuem_issue_tags","embeddable":true,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/issuem_issue_tags?post=634"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}