{"id":2921,"date":"2018-09-16T20:00:03","date_gmt":"2018-09-17T00:00:03","guid":{"rendered":"https:\/\/www.med.unc.edu\/bigs2?page_id=2921&#038;preview_id=2921"},"modified":"2020-10-13T17:41:49","modified_gmt":"2020-10-13T21:41:49","slug":"rmrss","status":"publish","type":"page","link":"https:\/\/www.med.unc.edu\/bigs2\/rmrss\/","title":{"rendered":"RMRSS: Regression Models on Riemannian Symmetric Spaces"},"content":{"rendered":"<div id=\"content1\">\n<div id=\"main\">\n<div id=\"right\">\n<div id=\"right_text\">\n<div class=\"box\">\n<p>The aim of this paper is to develop a general regression framework for\u00a0the analysis of manifold-valued response in a Riemannian symmetric space (RSS)\u00a0and its association with multiple covariates of interest, such as age or gender, in Euclidean space.\u00a0Such RSS-valued data arises frequently in medical imaging, surface modeling, and computer vision,\u00a0among many others. We develop an intrinsic regression model solely based on an intrinsic conditional moment assumption,\u00a0avoiding specifying any parametric distribution in RSS. We propose various link functions to\u00a0map from the Euclidean space of multiple covariates to the RSS of responses. We develop a two-stage procedure to calculate the\u00a0parameter estimates and\u00a0determine their asymptotic distributions. We construct the Wald and geodesic test statistics to\u00a0test hypotheses of unknown parameters. We systematically investigate the geometric\u00a0invariant property of these estimates and test statistics. Simulation studies and a real\u00a0data analysis are used to evaluate the finite sample properties of our methods.<\/p>\n<p><a href=\"https:\/\/www.med.unc.edu\/bigs2\/wp-content\/uploads\/sites\/822\/2018\/09\/ADNI_RMRSS.zip\"><strong>Software Download<\/strong> <\/a><\/p>\n<p><strong>Citation<\/strong>: Cornea, E., Zhu, H. T., Kim, P., and Ibrahim, J. G.\u00a0Intrinsic regression model for data in Riemannian symmetric space.\u00a0<em>Journal of the Royal Statistical Society B<\/em>, 2016.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"footer\">\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<p><!-- footer ends--><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>The aim of this paper is to develop a general regression framework for\u00a0the analysis of manifold-valued response in a Riemannian symmetric space (RSS)\u00a0and its association with multiple covariates of interest, such as age or gender, in Euclidean space.\u00a0Such RSS-valued data arises frequently in medical imaging, surface modeling, and computer vision,\u00a0among many others. We develop an &hellip; <a href=\"https:\/\/www.med.unc.edu\/bigs2\/rmrss\/\" aria-label=\"Read more about RMRSS: Regression Models on Riemannian Symmetric Spaces\">Read more<\/a><\/p>\n","protected":false},"author":55348,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-2921","page","type-page","status-publish","hentry","odd"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.8 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>RMRSS: Regression Models on Riemannian Symmetric Spaces - BIG-S2<\/title>\n<meta name=\"robots\" content=\"noindex, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"RMRSS: Regression Models on Riemannian Symmetric Spaces - BIG-S2\" \/>\n<meta property=\"og:description\" content=\"The aim of this paper is to develop a general regression framework for\u00a0the analysis of manifold-valued response in a Riemannian symmetric space (RSS)\u00a0and its association with multiple covariates of interest, such as age or gender, in Euclidean space.\u00a0Such RSS-valued data arises frequently in medical imaging, surface modeling, and computer vision,\u00a0among many others. We develop an &hellip; Read more\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.med.unc.edu\/bigs2\/rmrss\/\" \/>\n<meta property=\"og:site_name\" content=\"BIG-S2\" \/>\n<meta property=\"article:modified_time\" content=\"2020-10-13T21:41:49+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:\/\/www.med.unc.edu\/bigs2\/rmrss\/\",\"url\":\"https:\/\/www.med.unc.edu\/bigs2\/rmrss\/\",\"name\":\"RMRSS: Regression Models on Riemannian Symmetric Spaces - BIG-S2\",\"isPartOf\":{\"@id\":\"https:\/\/www.med.unc.edu\/bigs2\/#website\"},\"datePublished\":\"2018-09-17T00:00:03+00:00\",\"dateModified\":\"2020-10-13T21:41:49+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/www.med.unc.edu\/bigs2\/rmrss\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.med.unc.edu\/bigs2\/rmrss\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.med.unc.edu\/bigs2\/rmrss\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/www.med.unc.edu\/bigs2\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"RMRSS: Regression Models on Riemannian Symmetric Spaces\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.med.unc.edu\/bigs2\/#website\",\"url\":\"https:\/\/www.med.unc.edu\/bigs2\/\",\"name\":\"BIG-S2\",\"description\":\"Biostatistics and Imaging Genomics analysis lab - Statistics &amp; Signal\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.med.unc.edu\/bigs2\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"RMRSS: Regression Models on Riemannian Symmetric Spaces - BIG-S2","robots":{"index":"noindex","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"og_locale":"en_US","og_type":"article","og_title":"RMRSS: Regression Models on Riemannian Symmetric Spaces - BIG-S2","og_description":"The aim of this paper is to develop a general regression framework for\u00a0the analysis of manifold-valued response in a Riemannian symmetric space (RSS)\u00a0and its association with multiple covariates of interest, such as age or gender, in Euclidean space.\u00a0Such RSS-valued data arises frequently in medical imaging, surface modeling, and computer vision,\u00a0among many others. We develop an &hellip; Read more","og_url":"https:\/\/www.med.unc.edu\/bigs2\/rmrss\/","og_site_name":"BIG-S2","article_modified_time":"2020-10-13T21:41:49+00:00","twitter_card":"summary_large_image","twitter_misc":{"Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.med.unc.edu\/bigs2\/rmrss\/","url":"https:\/\/www.med.unc.edu\/bigs2\/rmrss\/","name":"RMRSS: Regression Models on Riemannian Symmetric Spaces - BIG-S2","isPartOf":{"@id":"https:\/\/www.med.unc.edu\/bigs2\/#website"},"datePublished":"2018-09-17T00:00:03+00:00","dateModified":"2020-10-13T21:41:49+00:00","breadcrumb":{"@id":"https:\/\/www.med.unc.edu\/bigs2\/rmrss\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.med.unc.edu\/bigs2\/rmrss\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.med.unc.edu\/bigs2\/rmrss\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.med.unc.edu\/bigs2\/"},{"@type":"ListItem","position":2,"name":"RMRSS: Regression Models on Riemannian Symmetric Spaces"}]},{"@type":"WebSite","@id":"https:\/\/www.med.unc.edu\/bigs2\/#website","url":"https:\/\/www.med.unc.edu\/bigs2\/","name":"BIG-S2","description":"Biostatistics and Imaging Genomics analysis lab - Statistics &amp; Signal","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.med.unc.edu\/bigs2\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"}]}},"_links_to":[],"_links_to_target":[],"_links":{"self":[{"href":"https:\/\/www.med.unc.edu\/bigs2\/wp-json\/wp\/v2\/pages\/2921","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.med.unc.edu\/bigs2\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.med.unc.edu\/bigs2\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.med.unc.edu\/bigs2\/wp-json\/wp\/v2\/users\/55348"}],"replies":[{"embeddable":true,"href":"https:\/\/www.med.unc.edu\/bigs2\/wp-json\/wp\/v2\/comments?post=2921"}],"version-history":[{"count":0,"href":"https:\/\/www.med.unc.edu\/bigs2\/wp-json\/wp\/v2\/pages\/2921\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.med.unc.edu\/bigs2\/wp-json\/wp\/v2\/media?parent=2921"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}