Admissible ways of merging p-values under arbitrary dependence
Vladimir Vovk, Bin Wang, Ruodu Wang
The Annals of Statistics · 2022 · Volume 50 · Issue 1
Abstract
Methods of merging several p-values into a single p-value are important in their own right and widely used in multiple hypothesis testing. This paper is the first to systematically study the admissibility (in Wald’s sense) of p-merging functions and their domination structure, without any information on the dependence structure of the input p-values. As a technical tool, we use the notion of e-values, which are alternatives to p-values recently promoted by several authors. We obtain several results on the representation of admissible p-merging functions via e-values and on (in)admissibility of existing p-merging functions. By introducing new admissible p-merging functions, we show that some classic merging methods can be strictly improved to enhance power without compromising validity under arbitrary dependence.
Keywords
62C15, 62F03, 62G10, admissible decisions, Duality, e-values, global null, multiple hypothesis testing
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