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Adaptive and dynamic adaptive procedures for false discovery rate control and estimation

Summary.  Many methods for estimation or control of the false discovery rate (FDR) can be improved by incorporating information about π0, the proportion of all tested null hypotheses that are true. Estimates of π0 are often based on the number of p‐values that exceed a threshold λ. We first give a finite sample proof for conservative point estimation of the FDR when the λ‐parameter is fixed. Then we establish a condition under which a dynamic adaptive procedure, whose λ‐parameter is determined by data, will lead to conservative π0‐ and FDR estimators. We also present asymptotic results on simultaneous conservative FDR estimation and control for a class of dynamic adaptive procedures. Simulation results show that a novel dynamic adaptive procedure achieves more power through smaller estimation errors for π0 under independence and mild dependence conditions. We conclude by discussing the connection between estimation and control of the FDR and show that several recently developed FDR control procedures can be cast in a unifying framework where the strength of the procedures can be easily evaluated.