Nicolai Meinshausen et al., ASYMPTOTIC OPTIMALITY OF THE WESTFALL-YOUNG PERMUTATION PROCEDURE FOR MULTIPLE TESTING UNDER DEPENDENCE, Annals of statistics , 39(6), 2011, pp. 3369-3391
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.