ADMISSIBLE WAYS OF MERGING P-VALUES UNDER ARBITRARY DEPENDENCE

• 成果类型: Article
• 署名作者: Vovk, Vladimir; Wang, Bin; Wang, Ruodu
• 署名单位: University of London; Royal Holloway University London; Chinese Academy of Sciences; University of Waterloo
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/21-AOS2109
• 发表日期: 2022
• 页码: 351-375
• 关键词: tests

摘要

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-emerging 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.