Simultaneous Testing of Grouped Hypotheses: Finding Needles in Multiple Haystacks
In 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...
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| Vydáno v: | Journal of the American Statistical Association Ročník 104; číslo 488; s. 1467 - 1481 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Alexandria, VA
Taylor & Francis
01.12.2009
American Statistical Association Assoc Taylor & Francis Ltd |
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| ISSN: | 0162-1459, 1537-274X |
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| Abstract | In 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. |
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| AbstractList | In 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. In 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. [PUBLICATION ABSTRACT] |
| Author | Sun, Wenguang Cai, T. Tony |
| Author_xml | – sequence: 1 givenname: T. Tony surname: Cai fullname: Cai, T. Tony – sequence: 2 givenname: Wenguang surname: Sun fullname: Sun, Wenguang |
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| Cites_doi | 10.1111/1467-9868.00346 10.1214/aoms/1177692621 10.1198/016214507000000545 10.1214/08-AOAS158 10.3102/10769986025001060 10.1093/biomet/93.3.509 10.1111/j.1467-9868.2008.00694.x 10.1177/144078302128756543 10.1093/biostatistics/5.2.155 10.1111/1467-9868.00347 10.1198/016214501753382129 10.1214/aos/1176342626 10.1214/009053604000000283 10.1111/j.1467-9868.2007.005592.x 10.1214/08-STS236D 10.1214/07-AOAS133 10.2307/2291733 10.1198/016214504000000089 10.1198/016214507000000167 10.1214/07-STS236 10.1214/07-AOAS141 |
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| Title | Simultaneous Testing of Grouped Hypotheses: Finding Needles in Multiple Haystacks |
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