Admissible ways of merging p-values under arbitrary dependence

Vladimir Vovk, Bin Wang, Ruodu Wang

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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
Issue number1
Publication statusPublished - 16 Feb 2022


  • p-values
  • duality
  • multiple hypothesis testing
  • admissibility
  • e-values

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