An Empirical Bayes Approach to Controlling the False Discovery Exceedance

TL;DR

This paper introduces an empirical Bayes method for controlling the false discovery exceedance in large-scale hypothesis testing, offering an alternative to FDR with improved control over variability.

Contribution

It develops a data-driven FDX control procedure based on an oracle rule, applicable to independent and certain dependent hypotheses, with demonstrated empirical effectiveness.

Findings

The proposed method effectively controls FDX in simulations.

It maximizes power under FDX constraints.

Application to stock trading data shows practical utility.

Abstract

In large-scale multiple hypothesis testing problems, the false discovery exceedance (FDX) provides a desirable alternative to the widely used false discovery rate (FDR) when the false discovery proportion (FDP) is highly variable. We develop an empirical Bayes approach to control the FDX. We show that, for independent hypotheses from a two-group model and dependent hypotheses from a Gaussian model fulfilling the exchangeability condition, an oracle decision rule based on ranking and thresholding the local false discovery rate (lfdr) is optimal in the sense that the power is maximized subject to the FDX constraint. We propose a data-driven FDX procedure that uses carefully designed computational shortcuts to emulate the oracle rule. We investigate the empirical performance of the proposed method using both simulated and real data and study the merits of FDX control through an application for identifying abnormal stock trading strategies.