“Multiple testing of discrete hypotheses with ordering information”
Abstract: In the last decade, motivated by a variety of applications in medicine, bioinformatics, genomics, brain imaging, etc., a growing amount of statistical research has been devoted to large-scale multiple testing, where thousands or even greater numbers of tests are conducted simultaneously. The false discovery rate (FDR) has been a popular measure used for error control in multiple testing. However, most existing FDR control procedures rely on the assumption that the p-values are continuously distributed as Uniform (0,1) under the null hypothesis. When tests are discrete, violation of this distributional assumption may lead to low detection power and inflated FDR. In this talk, we consider the discrete multiple testing with prior ordering information incorporated and propose a framework based on the marginal critical functions (MCFs) of randomized tests, which we prove to achieve asymptotic control of FDR or positive FDR. The theoretical properties of our procedures are carefully studied, and their performances are evaluated through various simulations and real applications with the analysis of genetic data from next-generation sequencing (NGS) experiments.
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