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

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.

Published in at http://dx.doi.org/10.1214/11-AOS946 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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• A Tutorial on Statistically Sound Pattern Discovery
• Permutation-based simultaneous confidence bounds for the false discovery proportion
• Efficient and powerful familywise error control in genome-wide association studies using generalized linear models