Combining p-values via averaging

• 成果类型: Article
• 署名作者: Vovk, Vladimir; Wang, Ruodu
• 署名单位: University of London; Royal Holloway University London; University of Waterloo
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asaa027
• 发表日期: 2020
• 页码: 791808
• 关键词: rejective multiple test; aggregation; bounds; tests

摘要

This paper proposes general methods for the problem of multiple testing of a single hypothesis, with a standard goal of combining a number of p-values without making any assumptions about their dependence structure. A result by Ruschendorf (1982) and, independently, Meng (1993) implies that the p-values can be combined by scaling up their arithmetic mean by a factor of 2, and no smaller factor is sufficient in general. A similar result by Mattner about the geometric mean replaces 2 by e. Based on more recent developments in mathematical finance, specifically, robust risk aggregation techniques, we extend these results to generalized means; in particular, we show thatK p-values can be combined by scaling up their harmonic mean by a factor of log K asymptotically as K tends to infinity. This leads to a generalized version of the Bonferroni-Holm procedure. We also explore methods using weighted averages of p-values. Finally, we discuss the efficiency of various methods of combining p-values and how to choose a suitable method in light of data and prior information.