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.
"Asymptotic optimality of the Westfall–Young permutation procedure for multiple testing under dependence." Ann. Statist. 39 (6) 3369 - 3391, December 2011. https://doi.org/10.1214/11-AOS946