Weighted p-value procedures for controlling FDR of grouped hypotheses

In this paper, we consider the multiple testing problems for grouped hypotheses. Two procedures are proposed based on weighted p-values, where the weights for p-values are obtained by maximizing a power-related objective function. We find that the proposed procedures can control the false discovery rate asymptotically, and are more powerful than existing methods asymptotically. We further examine their performances with extensive simulations. For illustration, we apply the proposed methods to the adequate yearly progress data.