False Discovery Rate Control Under General Dependence By Symmetrized Data Aggregation

TL;DR

This paper introduces a new distribution-free multiple testing method called the SDA filter that effectively controls the false discovery rate under general dependence, outperforming existing methods in power and robustness.

Contribution

The paper proposes a novel symmetrized data aggregation approach for FDR control that is robust under dependence and provides finite-sample and asymptotic guarantees.

Findings

SDA outperforms knockoff in power under dependence.

SDA is more robust than existing asymptotic p-value methods.

Numerical results show SDA's effectiveness and power gain.

Abstract

We develop a new class of distribution--free multiple testing rules for false discovery rate (FDR) control under general dependence. A key element in our proposal is a symmetrized data aggregation (SDA) approach to incorporating the dependence structure via sample splitting, data screening and information pooling. The proposed SDA filter first constructs a sequence of ranking statistics that fulfill global symmetry properties, and then chooses a data--driven threshold along the ranking to control the FDR. The SDA filter substantially outperforms the knockoff method in power under moderate to strong dependence, and is more robust than existing methods based on asymptotic $p$-values. We first develop finite--sample theory to provide an upper bound for the actual FDR under general dependence, and then establish the asymptotic validity of SDA for both the FDR and false discovery proportion (FDP) control under mild regularity conditions. The procedure is implemented in the R package \texttt{SDA}. Numerical results confirm the effectiveness and robustness of SDA in FDR control and show that it achieves substantial power gain over existing methods in many settings.