On optimality of the Benjamini-Hochberg procedure for the false discovery rate

The Benjamini-Hochberg step-up procedure controls the false discovery rate (FDR) provided the test statistics have a certain positive regression dependency. We show that this procedure controls the FDR under a weaker property and is optimal in the sense that its critical constants are uniformly greater than those of any step-up procedure with the FDR controlling property.