Admissible ways of merging p-values under arbitrary dependence. / Vovk, Vladimir; Wang, Bin; Wang, Ruodu.

In: The Annals of Statistics, Vol. 50, No. 1, 17.02.2022, p. 351-375.

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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.
Original languageEnglish
Pages (from-to)351-375
Number of pages25
JournalThe Annals of Statistics
Volume50
Issue number1
Publication statusPublished - 17 Feb 2022

ID: 42415583