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

TL;DR

This paper proves that the Westfall--Young permutation procedure achieves asymptotic optimality in power for large-scale multiple testing problems with dependent test statistics, especially under block dependence and sparsity.

Contribution

It establishes the asymptotic optimality of the Westfall--Young permutation method for dependent tests, extending its theoretical understanding in high-dimensional settings.

Findings

Westfall--Young method is asymptotically optimal under dependence.

The results apply to tests with block dependence and sparsity.

Permutation procedure maintains power in large-scale testing.

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.