Simultaneous false discovery rate control in location families

2026-05-10

AI Summary

This work addresses a limitation of conventional approaches in multiple hypothesis testing within location families, which typically control the false discovery rate (FDR) only under the global null hypothesis. In practice, however, there is often a need to control FDR uniformly over non-significant regions across the entire parameter space. The paper reframes FDR as a function of the location parameter and proposes a natural extension of the Benjamini–Hochberg (BH) procedure that simultaneously controls the entire FDR curve without incurring additional computational cost. Theoretical analysis establishes that the proposed method guarantees the FDR curve remains below a user-specified level uniformly, and numerical experiments corroborate its effectiveness and practical utility.

Abstract

When testing a number of statistical hypotheses using data from location families, it is often useful to control the false discovery rate (FDR) not just for hypotheses of the null values but also of other parameter values that are deemed practically insignificant. Here we consider FDR as a curve indexed by the location parameter and suggest a simple generalization of the Benjamini-Hochberg procedure that controls the FDR curve below any user-specified level. As a corollary of our main result, we show that the standard Benjamini-Hochberg procedure -- designed to control the FDR at the null -- also provides simultaneous control of the whole FDR curve for free. We further demonstrate the implications of our results and some practical considerations with a numerical example.

Problem

• false discovery rate
• location families
• multiple hypothesis testing
• FDR control
• Benjamini-Hochberg procedure

Innovation

• false discovery rate
• location families
• Benjamini-Hochberg procedure
• simultaneous inference
• FDR curve