Simultaneous Testing of Grouped Hypotheses: Finding Needles in Multiple Haystacks

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dc.contributor.authorCai, T. Tony
dc.contributor.authorSun, Wenguang
dc.date2023-05-17T15:02:05.000
dc.date.accessioned2023-05-23T03:36:56Z
dc.date.available2023-05-23T03:36:56Z
dc.date.issued2009-01-01
dc.date.submitted2016-07-15T12:56:21-07:00
dc.description.abstractIn large-scale multiple testing problems, data are often collected from heterogeneous sources and hypotheses form into groups that exhibit different characteristics. Conventional approaches, including the pooled and separate analyses, fail to efficiently utilize the external grouping information. We develop a compound decision theoretic framework for testing grouped hypotheses and introduce an oracle procedure that minimizes the false nondiscovery rate subject to a constraint on the false discovery rate. It is shown that both the pooled and separate analyses can be uniformly improved by the oracle procedure. We then propose a data-driven procedure that is shown to be asymptotically optimal. Simulation studies show that our procedures enjoy superior performance and yield the most accurate results in comparison with both the pooled and separate procedures. A real-data example with grouped hypotheses is studied in detail using different methods. Both theoretical and numerical results demonstrate that exploiting external information of the sample can greatly improve the efficiency of a multiple testing procedure. The results also provide insights on how the grouping information is incorporated for optimal simultaneous inference.
dc.identifier.urihttps://repository.upenn.edu/handle/20.500.14332/47880
dc.legacy.articleid1108
dc.legacy.fields10.1198/jasa.2009.tm08415
dc.legacy.fulltexturlhttps://repository.upenn.edu/cgi/viewcontent.cgi?article=1108&context=statistics_papers&unstamped=1
dc.rightsThis is an Accepted Manuscript of an article published by Taylor & Francis in Journal of the American Statistical Association on 01 Jan 2012, available online: http://wwww.tandfonline.com/10.1198/jasa.2009.tm08415.
dc.source.beginpage1467
dc.source.endpage1481
dc.source.issue489
dc.source.issue488
dc.source.journalStatistics Papers
dc.source.journaltitleJournal of the American Statistical Association
dc.source.statuspublished
dc.source.volume104
dc.subject.othercompound decision problem
dc.subject.otherconditional local false discovery rate
dc.subject.otherexchangeability
dc.subject.otherfalse discovery rate
dc.subject.othergrouped hypotheses
dc.subject.otherlarge-scale multiple testing
dc.subject.otherStatistics and Probability
dc.titleSimultaneous Testing of Grouped Hypotheses: Finding Needles in Multiple Haystacks
dc.typeArticle
digcom.contributor.authorCai, T. Tony
digcom.contributor.authorSun, Wenguang
digcom.identifierstatistics_papers/489
digcom.identifier.contextkey8840384
digcom.identifier.submissionpathstatistics_papers/489
digcom.typearticle
dspace.entity.typePublication
upenn.schoolDepartmentCenterStatistics Papers
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