{"id":9896,"date":"2022-11-22T10:09:56","date_gmt":"2022-11-22T09:09:56","guid":{"rendered":"https:\/\/ensai.fr\/?p=9896"},"modified":"2022-11-22T10:09:56","modified_gmt":"2022-11-22T09:09:56","slug":"saumard-annals-of-statistics","status":"publish","type":"post","link":"https:\/\/ensai.fr\/en\/saumard-annals-of-statistics\/","title":{"rendered":"Relaxing the Gaussian assumption in shrinkage and SURE in high dimension \u2013 Annals of Statistics\u00a0"},"content":{"rendered":"<p><b><span data-contrast=\"auto\">Co-authored by Max Fathi, Larry Goldstein, Gesine Reinert, and <\/span><\/b><a href=\"https:\/\/ensai.fr\/en\/equipe\/adrien-saumard\/\"><b><span data-contrast=\"none\">Adrien Saumard<\/span><\/b><\/a><b><span data-contrast=\"auto\">, associate professor of Statistics at ENSAI and researcher at CREST, the paper \u201cRelaxing the Gaussian assumption in shrinkage and SURE in high dimension\u201d was published in <\/span><\/b><a href=\"https:\/\/doi.org\/10.1214\/22-AOS2208\"><b><span data-contrast=\"none\">volume 50 of the Annals of Statistics<\/span><\/b><\/a><b><span data-contrast=\"auto\">.\u00a0<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<p><span data-contrast=\"auto\">The Annals of Statistics is a peer-reviewed Statistics <\/span><a href=\"https:\/\/en.wikipedia.org\/wiki\/Academic_journal\"><span data-contrast=\"none\">journal<\/span><\/a><span data-contrast=\"auto\"> published by the <\/span><a href=\"https:\/\/en.wikipedia.org\/wiki\/Institute_of_Mathematical_Statistics\"><span data-contrast=\"none\">Institute of Mathematical Statistics<\/span><\/a><span data-contrast=\"auto\">.\u00a0<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<h3>Abstract<\/h3>\n<p><span data-contrast=\"auto\">Shrinkage estimation is a fundamental tool of modern statistics, pioneered by Charles Stein upon his discovery of the famous paradox involving the multivariate Gaussian. A large portion of the subsequent literature only considers the efficiency of shrinkage, and that of an associated procedure known as Stein\u2019s Unbiased Risk Estimate, or SURE, in the Gaussian setting of that original work. We investigate what extensions to the domain of validity of shrinkage and SURE can be made away from the Gaussian through the use of tools developed in the probabilistic area now known as Stein\u2019s method. We show that shrinkage is efficient away from the Gaussian under very mild conditions on the distribution of the noise. SURE is also proved to be adaptive under similar assumptions, and in particular in a way that retains the classical asymptotics of Pinsker\u2019s theorem. Notably, shrinkage and SURE are shown to be efficient under mild distributional assumptions, and particularly for general isotropic log-concave measures.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<h3>Keywords<\/h3>\n<p><span data-contrast=\"auto\">shrinkage estimation, Stein kernel, unbiased risk estimation, zero bias<\/span><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<h3>Author Affiliations<\/h3>\n<p><span data-contrast=\"auto\">Max Fathi: Universit\u00e9 Paris Cit\u00e9 and Sorbonne Universit\u00e9, CNRS, Laboratoire Jacques-Louis Lions &amp; Laboratoire de Probabilit\u00e9s, Statistique et Mod\u00e9lisation<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<p><span data-contrast=\"auto\">Larry Goldstein: Department of Mathematics, University of Southern California<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<p><span data-contrast=\"auto\">Gesine Reinert: Department of Statistics, University of Oxford<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n<p><span data-contrast=\"auto\">Adrien Saumard: ENSAI, CREST-UMR 9194<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span class=\"hentry_link_contour\"><a href=\"https:\/\/doi.org\/10.1214\/22-AOS2208\" target=\"_blank\" rel=\"noopener noreferrer\">Download the article<\/a><\/span><\/p>\n<p>&nbsp;<\/p>\n<p><b><i><span data-contrast=\"none\">Find out more about <\/span><\/i><\/b><a href=\"https:\/\/ensai.fr\/en\/equipe\/adrien-saumard\/\"><b><i><span data-contrast=\"none\">Adrien Saumard<\/span><\/i><\/b><\/a> <b><i><span data-contrast=\"auto\">a<\/span><\/i><\/b><b><i><span data-contrast=\"none\">nd <\/span><\/i><\/b><a href=\"https:\/\/ensai.fr\/en\/recherche\/themes-de-recherche\/\"><b><i><span data-contrast=\"none\">research at ENSAI<\/span><\/i><\/b><\/a><b><i><span data-contrast=\"none\">.<\/span><\/i><\/b><span data-ccp-props=\"{&quot;134233117&quot;:false,&quot;134233118&quot;:false,&quot;201341983&quot;:0,&quot;335551550&quot;:1,&quot;335551620&quot;:1,&quot;335559685&quot;:0,&quot;335559737&quot;:0,&quot;335559738&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:259}\">\u00a0<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Co-authored by Max Fathi, Larry Goldstein, Gesine Reinert, and Adrien Saumard, associate&#8230; <br \/><a class=\"readmore\" href=\"https:\/\/ensai.fr\/en\/saumard-annals-of-statistics\/\">Lire la suite<\/a><\/p>\n","protected":false},"author":73,"featured_media":9904,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[185],"tags":[342],"class_list":["post-9896","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-research-innovation","tag-publication"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Relaxing the Gaussian assumption in shrinkage and SURE in high dimension \u2013 Annals of Statistics\u00a0 | ENSAI<\/title>\n<meta name=\"description\" content=\"Co-authored by Max Fathi, Larry Goldstein, Gesine Reinert, and Adrien Saumard, associate professor of Statistics at ENSAI and researcher at CREST, the paper \u201cRelaxing the Gaussian assumption in shrinkage and SURE in high dimension\u201d was published in volume 50 of the Annals of Statistics.\u00a0\u00a0\" 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