Is Bonferroni Admissible for Large m?

Modern methods of multiple comparisons, particularly those based on controlling the false discovery rate, are lax relative to the Bonferroni method in their assignment of significances; they are relatively more lax as m, the number of tests, increases. We point out that this laxness is based on an assumption concerning the size of the loss due to Type I errors relative to the loss due to Type II errors, and challenge the generality of this assumption, providing an alternative loss function for which the Bonferroni method is asymptotically (as m → ∞) optimal.