  Familywise error rate (FWER) has been a cornerstone in simultaneous inference
for decades, and the classical Bonferroni method has been one of the most
prominent frequentist approaches for controlling FWER. The present article
studies the limiting behavior of Bonferroni FWER in a multiple testing problem
as the number of hypotheses grows to infinity. We establish that in the
equicorrelated normal setup with positive equicorrelation, Bonferroni FWER
tends to zero asymptotically. We extend this result for generalized familywise
error rates and to arbitrarily correlated setups.
