{"title":"稀疏性条件下多元正态均值多重检验的贝叶斯神谕特性","authors":"Zikun Qin, Malay Ghosh","doi":"10.1016/j.jspi.2024.106227","DOIUrl":null,"url":null,"abstract":"<div><p>The paper considers a multiple testing problem of multivariate normal means under sparsity. First, the Bayes risk of the multivariate Bayes oracle is derived. Then, a hierarchical Bayesian approach is taken with global–local shrinkage priors, where the global parameter is either treated as a tuning parameter or is given a specific prior. The method is shown to attain an asymptotic Bayes optimal under sparsity (ABOS) property. Finally, an empirical Bayes procedure is proposed which involves estimation of the global shrinkage parameter. The approach is also shown to lead to the ABOS property.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Bayes oracle property of multiple tests of multivariate normal means under sparsity\",\"authors\":\"Zikun Qin, Malay Ghosh\",\"doi\":\"10.1016/j.jspi.2024.106227\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The paper considers a multiple testing problem of multivariate normal means under sparsity. First, the Bayes risk of the multivariate Bayes oracle is derived. Then, a hierarchical Bayesian approach is taken with global–local shrinkage priors, where the global parameter is either treated as a tuning parameter or is given a specific prior. The method is shown to attain an asymptotic Bayes optimal under sparsity (ABOS) property. Finally, an empirical Bayes procedure is proposed which involves estimation of the global shrinkage parameter. The approach is also shown to lead to the ABOS property.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-08-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0378375824000843\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0378375824000843","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
本文研究了稀疏性条件下的多元正态均值多重检验问题。首先,推导出多元贝叶斯神谕的贝叶斯风险。然后,采用全局-局部收缩先验的分层贝叶斯方法,其中全局参数要么被视为调整参数,要么被赋予特定先验。结果表明,该方法具有稀疏性下的渐进贝叶斯最优(ABOS)特性。最后,提出了一种经验贝叶斯程序,涉及全局收缩参数的估计。该方法也显示出 ABOS 特性。
Bayes oracle property of multiple tests of multivariate normal means under sparsity
The paper considers a multiple testing problem of multivariate normal means under sparsity. First, the Bayes risk of the multivariate Bayes oracle is derived. Then, a hierarchical Bayesian approach is taken with global–local shrinkage priors, where the global parameter is either treated as a tuning parameter or is given a specific prior. The method is shown to attain an asymptotic Bayes optimal under sparsity (ABOS) property. Finally, an empirical Bayes procedure is proposed which involves estimation of the global shrinkage parameter. The approach is also shown to lead to the ABOS property.