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

Optimal weighting for false discovery rate control

How to weigh the Benjamini-Hochberg procedure? In the context of multiple hypothesis testing, we propose a new step-wise procedure that controls the false discovery rate (FDR) and we prove it to be more powerful than any weighted Benjamini-Hochberg procedure. Both finitesample and asymptotic results are presented. Moreover, we illustrate good performance of our procedure in simulations and a ge...

Controlling the Number of False Positives Using the Benjamini- Hochberg FDR Procedure Paul N. Somerville University of Central Florida Controlling the Number of False Positives Using the Benjamini- Hochberg FDR Procedure

On Signal Detection Using the Benjamini-hochberg Procedure

We investigate a multiple hypothesis test designed for detecting signals embedded in noisy observations of a sensor array. The global level of the multiple test is controlled by the false discovery rate (FDR) criterion recently suggested by Benjamini and Hochberg instead of the classical familywise error rate (FWE) criterion. In the previous study [3], the suggested procedure has shown promisin...

A New Proof of FDR Control Based on Forward Filtration

For multiple testing problems, Benjamini and Hochberg (1995) proposed the false discovery rate (FDR) as an alternative to the family-wise error rate (FWER). Since then, researchers have provided many proofs to control the FDR under different assumptions. Storey et al. (2004) showed that the rejection threshold of a BH step-up procedure is a stopping time with respect to the reverse filtration g...

Bayesian Multiple Testing under Sparsity for Polynomial-tailed Distributions

This paper considers Bayesian multiple testing under sparsity for polynomial-tailed distributions satisfying a monotone likelihood ratio property. Included in this class of distributions are the Student’s t, the Pareto, and many other distributions. We prove some general asymptotic optimality results under fixed and random thresholding. As examples of these general results, we establish the Bay...