A Compound Decision-Theoretic Approach to Large-Scale Multiple Testing
T. Tony Cai and Wenguang Sun
In this article, we discuss topics in large-scale multiple testing and present a compound decision theoretical framework for false discovery rate (FDR) analysis. It is shown that conventional multiple testing procedures that threshold p-values can be much improved by a class of powerful data-driven procedures that exploit relevant information of the sample, including the proportion of non-nulls, the null and alternative distributions, the correlation structures as well as possible external information. Our discussion reveals the special features of large-scale inference problems and provides additional insights into the classic statistical decision theory. Both simulated and real data examples are presented for illustration of ideas and comparison of different procedures. Some important open problems for future research are also discussed.