  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.
