Approximating Familywise Error Rate for Correlated Normal

We study the limiting behavior of the familywise error rate (FWER) of the Bonferroni procedure in a multiple testing problem. We establish that, in the equicorrelated normal setup, the FWER of Bonferroni's method tends to zero asymptotically (i.e for a sufficiently large number of hypotheses) for any positive equicorrelation. We extend this result for generalized familywise error rates.