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