Abstract
The Benjamin--Hochberg (BH) procedure and many of its generalizations are empirically observed to control the false discovery rate (FDR) much beyond the regimes that are known to enjoy provable FDR control. To address this gap, this talk introduces some new results that imply the robustness of the BH procedure and certain related procedures for FDR control. First, we show that FDR control is maintained up to a small multiplicative factor under arbitrary dependence between false null test statistics and independent true null test statistics. The proof technique is based on a new backward submartingale argument. Next, we further extend the FDR control to the case where the null test statistics exhibit certain positive dependence, implying that the null distribution plays an essential role in FDR control. We conclude the talk by introducing a weak version of FDR control for which the BH procedure is robust against any adversarial false null test statistics. Part of this talk is based on joint work with Cynthia Dwork (Harvard) and Li Zhang (Google).