Admissible ways of merging p-values under arbitrary dependence (Bin Wang)

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05 12, 2022

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.


Publication:

Annals of Statistics 50(1): 351-375 (February 2022)


Author:

Vladimir Vovk

Department of Computer Science, Royal Holloway, University of London, Egham, Surrey, UK.

E-mail: v.vovk@rhul.ac.uk

 

Bin Wang

RCSDS, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China.

E-mail: wangbin@amss.ac.cn

 

Ruodu Wang

Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada.

E-mail: wang@uwaterloo.ca

Contacts:

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