Dynamic adaptive procedures that control the false discovery rate

TL;DR

This paper introduces dynamic adaptive procedures for controlling the false discovery rate in multiple testing, where tuning parameters are data-dependent, ensuring finite-sample FDR control and demonstrating improved power in simulations.

Contribution

It develops theoretical foundations for dynamic adaptive procedures with data-driven tuning, including the right-boundary and lowest-slope methods, ensuring finite-sample FDR control.

Findings

Right-boundary procedure outperforms others in power

Finite-sample FDR control is achieved with data-dependent tuning

Procedures are effective under independence and mild dependence

Abstract

In the multiple testing problem with independent tests, the classical linear step-up procedure controls the false discovery rate (FDR) at level $\pi_0\alpha$, where $\pi_0$ is the proportion of true null hypotheses and $\alpha$ is the target FDR level. Adaptive procedures can improve power by incorporating estimates of $\pi_0$, which typically rely on a tuning parameter. Fixed adaptive procedures set their tuning parameters before seeing the data and can be shown to control the FDR in finite samples. We develop theoretical results for dynamic adaptive procedures whose tuning parameters are determined by the data. We show that, if the tuning parameter is chosen according to a left-to-right stopping time rule, the corresponding dynamic adaptive procedure controls the FDR in finite samples. Examples include the recently proposed right-boundary procedure and the widely used lowest-slope procedure, among others. Simulation results show that the right-boundary procedure is more powerful than other dynamic adaptive procedures under independence and mild dependence conditions.