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.
Funding Statement
V. Vovk’s research has been partially supported by Amazon, Astra Zeneca and Stena Line. R. Wang is supported by the Natural Sciences and Engineering Research Council of Canada (RGPIN-2018-03823, RGPAS-2018-522590).
Acknowledgments
We are grateful to the Editor, an Associate Editor, and three anonymous referees for very helpful comments. Many thanks to Wesley Tansey for useful discussions.
Citation
Vladimir Vovk. Bin Wang. Ruodu Wang. "Admissible ways of merging p-values under arbitrary dependence." Ann. Statist. 50 (1) 351 - 375, February 2022. https://doi.org/10.1214/21-AOS2109
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