title: The optimal power puzzle: scrutiny of the monotone likelihood ratio assumption in multiple testing.
abstract: In single hypothesis testing, power is a non-decreasing function of type I error rate; hence it is desirable to test at the nominal level exactly to achieve optimal power. The puzzle lies in the fact that for multiple testing, under the false discovery rate paradigm, such a monotonic relationship may not hold. In particular, exact false discovery rate control may lead to a less powerful testing procedure if a test statistic fails to fulfil the monotone likelihood ratio condition. In this article, we identify different scenarios wherein the condition fails and give caveats for conducting multiple testing in practical settings.
authors.affiliation: Department of Health Studies, University of Chicago, Chicago, Illinois 60637, U.S.A.
authors.forename: Hongyuan
authors.initials: H
authors.lastname: Cao
authors.affiliation: Department of Information and Operation Management, Marshall School of Business, University of Southern California, Los Angeles, California 90089, U.S.A.
authors.forename: Wenguang
authors.initials: W
authors.lastname: Sun
authors.affiliation: Department of Biostatistics and Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27514, U.S.A.
authors.forename: Michael R
authors.initials: MR
authors.lastname: Kosorok
keywords: False discovery rate; heteroscedasticity; monotone likelihood ratio; multiple testing dependence
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