Date of this Version
Journal of the American Statistical Association
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.
This 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.
compound decision problem, conditional local false discovery rate, exchangeability, false discovery rate, grouped hypotheses, large-scale multiple testing
Cai, T., & Sun, W. (2009). Simultaneous Testing of Grouped Hypotheses: Finding Needles in Multiple Haystacks. Journal of the American Statistical Association, 104 (488), 1467-1481. http://dx.doi.org/10.1198/jasa.2009.tm08415
Date Posted: 27 November 2017