Abstract：Suppose there are a large scale hypotheses with two-sided alternatives to be tested simultaneously. The directional decision is required to be made once a null hypothesis is rejected. In this case the mixed directional false discovery rate (mdFDR) is preferable to the usual FDR for the former allowing to control the sum of expected proportions of Type I and Type III errors among all rejections. Existing literature showed the directional BH procedure (dBH procedure)， which is the BH linear step-up procedure being with directional decisions according to the signs of testing statistics， can control mdFDR at the significant level α. Besides the dBH procedure， a procedure proposed by Sarkar and Zhou (SZ procedure) also can control the mdFDR. Sarkar and Zhou showed the optimality of their procedure from the Bayesian point of view. In this paper， we discuss the optimality of the SZ procedure from the frequentist point of view which assumes the hypotheses distributions can be learned from the data. By our discussion， the SZ procedure is still optimal in the sense of controlling mdFDR and correctly declaring more non-null hypotheses.Simulation results further verify that the analytical results hold and the SZ procedure is more efficient than the dBH procedure.
2018, Vol. 52 
