Asymptotic optimality of the Westfall–Young permutation procedure for multiple testing under dependence

Nicolai Meinshausen, Marloes H. Maathuis, Peter Bühlmann

The Annals of Statistics · 2011 · Volume 39 · Issue 6

Abstract

Test statistics are often strongly dependent in large-scale multiple testing applications. Most corrections for multiplicity are unduly conservative for correlated test statistics, resulting in a loss of power to detect true positives. We show that the Westfall–Young permutation method has asymptotically optimal power for a broad class of testing problems with a block-dependence and sparsity structure among the tests, when the number of tests tends to infinity.

Keywords

62F03, 62J15, asymptotic optimality, familywise error rate, high-dimensional inference, Multiple testing under dependence, permutations, rank-based nonparametric tests, Sparsity, Westfall–Young procedure

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