{"id":670,"date":"2017-09-28T08:41:43","date_gmt":"2017-09-28T08:41:43","guid":{"rendered":"http:\/\/jsr.isrt.ac.bd\/?post_type=article&#038;p=670"},"modified":"2017-09-28T08:45:30","modified_gmt":"2017-09-28T08:45:30","slug":"estimation-variance-anova-setup","status":"publish","type":"article","link":"http:\/\/jsr.isrt.ac.bd\/article\/estimation-variance-anova-setup\/","title":{"rendered":"Estimation of variance in an ANOVA setup"},"content":{"rendered":"<p>In an ANOVA setup one tests the global null hypothesis against the alternative<br \/>\nthat at least one pair of means differ. In this paper we consider the estimation of<br \/>\nthe variance, when it is suspected, but one is not sure, that the null hypothesis<br \/>\nholds. We consider the (i) unrestricted unbiased estimator (UUE), (ii) unrestricted<br \/>\nbiased estimator (UBE), (iii) restricted unbiased estimator (RUE), (iv)<br \/>\nrestricted biased estimator (RBE), (v) preliminary test estimator (PTE) using<br \/>\nUUE and RUE, (vi) Stein-type estimator (SE) using UBE and RBE of variance.<br \/>\nWe derive the bias and risk expressions for these estimators to compare them. It<br \/>\nis shown that Stein-type estimator (SE) dominates uniformly over the UUE as<br \/>\nwell as the PTE when the critical value for preliminary test is 1.<\/p>\n<p><a href=\"http:\/\/jsr.isrt.ac.bd\/wp-content\/uploads\/39n2_8.pdf\">Fulltext<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In an ANOVA setup one tests the global null hypothesis against the alternative that at least one pair of means differ. In this paper we consider the estimation of the variance, when it is suspected, but one is not sure, that the null hypothesis holds. We consider the (i) unrestricted unbiased estimator (UUE), (ii) unrestricted [&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 variance in an ANOVA setup - 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-variance-anova-setup\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Estimation of variance in an ANOVA setup - JSR\" \/>\n<meta property=\"og:description\" content=\"In an ANOVA setup one tests the global null hypothesis against the alternative that at least one pair of means differ. In this paper we consider the estimation of the variance, when it is suspected, but one is not sure, that the null hypothesis holds. We consider the (i) unrestricted unbiased estimator (UUE), (ii) unrestricted [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/jsr.isrt.ac.bd\/article\/estimation-variance-anova-setup\/\" \/>\n<meta property=\"og:site_name\" content=\"JSR\" \/>\n<meta property=\"article:modified_time\" content=\"2017-09-28T08:45:30+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-variance-anova-setup\/\",\"url\":\"https:\/\/jsr.isrt.ac.bd\/article\/estimation-variance-anova-setup\/\",\"name\":\"Estimation of variance in an ANOVA setup - JSR\",\"isPartOf\":{\"@id\":\"https:\/\/jsr.isrt.ac.bd\/#website\"},\"datePublished\":\"2017-09-28T08:41:43+00:00\",\"dateModified\":\"2017-09-28T08:45:30+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/jsr.isrt.ac.bd\/article\/estimation-variance-anova-setup\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/jsr.isrt.ac.bd\/article\/estimation-variance-anova-setup\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/jsr.isrt.ac.bd\/article\/estimation-variance-anova-setup\/#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 variance in an ANOVA setup\"}]},{\"@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 variance in an ANOVA setup - 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-variance-anova-setup\/","og_locale":"en_US","og_type":"article","og_title":"Estimation of variance in an ANOVA setup - JSR","og_description":"In an ANOVA setup one tests the global null hypothesis against the alternative that at least one pair of means differ. In this paper we consider the estimation of the variance, when it is suspected, but one is not sure, that the null hypothesis holds. We consider the (i) unrestricted unbiased estimator (UUE), (ii) unrestricted [&hellip;]","og_url":"https:\/\/jsr.isrt.ac.bd\/article\/estimation-variance-anova-setup\/","og_site_name":"JSR","article_modified_time":"2017-09-28T08:45:30+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-variance-anova-setup\/","url":"https:\/\/jsr.isrt.ac.bd\/article\/estimation-variance-anova-setup\/","name":"Estimation of variance in an ANOVA setup - JSR","isPartOf":{"@id":"https:\/\/jsr.isrt.ac.bd\/#website"},"datePublished":"2017-09-28T08:41:43+00:00","dateModified":"2017-09-28T08:45:30+00:00","breadcrumb":{"@id":"https:\/\/jsr.isrt.ac.bd\/article\/estimation-variance-anova-setup\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/jsr.isrt.ac.bd\/article\/estimation-variance-anova-setup\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/jsr.isrt.ac.bd\/article\/estimation-variance-anova-setup\/#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 variance in an ANOVA setup"}]},{"@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\/670"}],"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=670"}],"version-history":[{"count":0,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/article\/670\/revisions"}],"wp:attachment":[{"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/media?parent=670"}],"wp:term":[{"taxonomy":"issuem_issue","embeddable":true,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/issuem_issue?post=670"},{"taxonomy":"issuem_issue_categories","embeddable":true,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/issuem_issue_categories?post=670"},{"taxonomy":"issuem_issue_tags","embeddable":true,"href":"http:\/\/jsr.isrt.ac.bd\/wp-json\/wp\/v2\/issuem_issue_tags?post=670"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}