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

In: The Annals of Statistics, 15.06.2021.

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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
JournalThe Annals of Statistics
Publication statusAccepted/In press - 15 Jun 2021

ID: 42415583