Combining P-Values Via Averaging

Forthcoming, Biometrika

29 Pages Posted: 17 May 2018 Last revised: 14 Dec 2019

See all articles by Vladimir Vovk

Vladimir Vovk

University of London - Royal Holloway College

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Date Written: April 20, 2018

Abstract

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. An old result by Ruschendorf and, independently, Meng 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). Based on more recent developments in mathematical finance, specifically, robust risk aggregation techniques, we show that K p-values can be combined by scaling up their geometric mean by a factor of e (for all K) and by scaling up their harmonic mean by a factor of ln K (asymptotically as K -> infinity). These and other results lead to a generalized version of the Bonferroni-Holm method. A simulation study compares the performance of various averaging methods.

Keywords: hypothesis testing, multiple hypothesis testing, multiple testing of a single hypothesis, robust risk aggregation

JEL Classification: C12

Suggested Citation

Vovk, Vladimir and Wang, Ruodu, Combining P-Values Via Averaging (April 20, 2018). Forthcoming, Biometrika, Available at SSRN: https://ssrn.com/abstract=3166304 or http://dx.doi.org/10.2139/ssrn.3166304

Vladimir Vovk

University of London - Royal Holloway College ( email )

Egham
Surrey
TW20 0EX
United Kingdom

Ruodu Wang (Contact Author)

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

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