Admissible ways of merging p-values under arbitrary dependence
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.
Keywords
Cite
@article{arxiv.2007.14208,
title = {Admissible ways of merging p-values under arbitrary dependence},
author = {Vladimir Vovk and Bin Wang and Ruodu Wang},
journal= {arXiv preprint arXiv:2007.14208},
year = {2021}
}
Comments
43 pages and 9 figures; as compared with the previous version, there are numerous improvements and further simulation studies