{"id":2466,"date":"2024-11-16T22:00:32","date_gmt":"2024-11-16T14:00:32","guid":{"rendered":"https:\/\/changjinyuan.com\/?p=2466"},"modified":"2024-12-28T23:09:52","modified_gmt":"2024-12-28T15:09:52","slug":"jinyuan-chang-shao-q-m-zhou-w-x-2016-cramer-type-moderate-deviations-for-studentized-two-sample-u-statistics-with-applications-the-annals-of-statistics-44-1931-1956","status":"publish","type":"post","link":"https:\/\/changjinyuan.com\/index.php\/en\/publications-en\/publications-all-en\/2466\/","title":{"rendered":"Chang, J., Shao, Q. M., &#038; Zhou, W. X. (2016). Cram\u00e9r-type moderate deviations for Studentized two-sample U-statistics with applications. The Annals of Statistics, 44, 1931-1956."},"content":{"rendered":"<p>Two-sample U -statistics are widely used in a broad range of applications, including those in the fields of biostatistics and econometrics. In this paper, we establish sharp Crame\u0301r-type moderate deviation theorems for Studentized two-sample U-statistics in a general framework, including the two-sample t-statistic and Studentized Mann\u2013Whitney test statistic as prototypical exam- ples. In particular, a refined moderate deviation theorem with second-order accuracy is established for the two-sample t-statistic. These results extend the applicability of the existing statistical methodologies from the one-sample t-statistic to more general nonlinear statistics. Applications to two-sample large-scale multiple testing problems with false discovery rate control and the regularized bootstrap method are also discussed.<\/p>\r\n\r\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" style=\"width: 100%; height: 600px;\" data=\"https:\/\/changjinyuan.com\/wp-content\/uploads\/2024\/12\/Cramer-type-moderate-deviations-for-Studentized-two-sample-U-statistics-with-applications.pdf\" type=\"application\/pdf\" width=\"300\" height=\"150\" aria-label=\"\u5d4c\u5165 &lt;strong&gt;&lt;mark style=&quot;background-color:rgba(0, 0, 0, 0)&quot; class=&quot;has-inline-color has-vivid-cyan-blue-color&quot;&gt;Cramer-type moderate deviations for Studentized two-sample U-statistics with applications.pdf&lt;\/mark&gt;&lt;\/strong&gt;\"><\/object><a id=\"wp-block-file--media-6323e4ea-a450-4f55-ae61-c367526c293e\" href=\"https:\/\/changjinyuan.com\/wp-content\/uploads\/2024\/12\/Cramer-type-moderate-deviations-for-Studentized-two-sample-U-statistics-with-applications.pdf\"><strong><mark class=\"has-inline-color has-vivid-cyan-blue-color\" style=\"background-color: rgba(0, 0, 0, 0);\">Cramer-type moderate deviations for Studentized two-sample U-statistics with applications.pdf<\/mark><\/strong><\/a><a class=\"wp-block-file__button wp-element-button\" href=\"https:\/\/changjinyuan.com\/wp-content\/uploads\/2024\/12\/Cramer-type-moderate-deviations-for-Studentized-two-sample-U-statistics-with-applications.pdf\" download=\"\" aria-describedby=\"wp-block-file--media-6323e4ea-a450-4f55-ae61-c367526c293e\">Download<\/a><\/div>","protected":false},"excerpt":{"rendered":"<p>Two-sample U -statistics are widely used in a broad range of applications, including those in the fields of biostatistics and econometrics. In this paper, we establish sharp Crame\u0301r-type moderate deviation theorems for Studentized two-sample U-statistics in a general framework, including the two-sample t-statistic and Studentized Mann\u2013Whitney test statistic as prototypical exam- ples. In particular, a refined moderate deviation theorem with second-order accuracy is established for the two-sample t-statistic. These results extend the applicability of the existing statistical methodologies from the one-sample t-statistic to more general nonlinear statistics. Applications to two-sample large-scale multiple testing problems with false discovery rate control and the regularized bootstrap method are also discussed.<\/p>\n","protected":false},"author":1,"featured_media":2457,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[21],"tags":[],"class_list":["post-2466","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-publications-all-en"],"acf":[],"lang":"en","translations":{"en":2466,"cn":2456},"pll_sync_post":[],"_links":{"self":[{"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/posts\/2466","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/comments?post=2466"}],"version-history":[{"count":4,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/posts\/2466\/revisions"}],"predecessor-version":[{"id":3931,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/posts\/2466\/revisions\/3931"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/media\/2457"}],"wp:attachment":[{"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/media?parent=2466"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/categories?post=2466"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/changjinyuan.com\/index.php\/wp-json\/wp\/v2\/tags?post=2466"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}