A decision theoretic approach to optimization of multiple testing procedures

Journal article, 2015

This paper focuses on the concept of optimizing a multiple testing procedure (MTP) with respect to a predefined utility function. The class of Bonferroni-based closed testing procedures, which includes, for example, (weighted) Holm, fallback, gatekeeping, and recycling/graphical procedures, is used in this context. Numerical algorithms for calculating expected utility for some MTPs in this class are given. The obtained optimal procedures, as well as the gain resulting from performing an optimization are then examined in a few, but informative, examples.