Generalized Boundary FDR Control under Arbitrary Dependence: An Approach on Closure Principle

2026-05-11

AI Summary

Traditional false discovery rate (FDR) methods struggle to ensure the reliability of “marginal discoveries” within rejection sets, while existing bounded FDR (bFDR) control approaches rely on strong assumptions such as independence or specific priors. This work introduces the k-bFDR criterion to control the error rate among the k least significant discoveries and provides, for the first time, a generalized definition that establishes theoretical connections with existing error metrics. Building upon the closure principle, we develop the Domino framework—a unified procedure that rigorously controls k-bFDR for both p-values and e-values under arbitrary dependence structures. Theoretical analysis and empirical experiments demonstrate that our method effectively maintains error rate control across diverse dependency scenarios and yields higher-quality, more practically meaningful rejection sets in real-data analyses.

Abstract

False discovery rate (FDR) is a cornerstone of modern multiple testing. However, it often fails to guarantee the reliability of "marginal" discoveries that lie at the boundary of the rejection set, which are often crucial in high-precision applications. While recent works (Soloff et al., 2024; Xiang et al., 2025) introduced the boundary false discovery rate (bFDR) to control the error probability at the marginal discovery, their method relies on restrictive assumptions such as independence or specific prior distributions. In this paper, we first propose $k$-bFDR, a novel generalization that controls the error probability of the $k$ least significant discoveries. We then provide a systematic investigation into the theoretical relationship between $k$-bFDR and existing error metrics. Furthermore, building upon the closure principle, we develop Domino, a unified framework that guarantees $k$-bFDR control under arbitrary dependence, applicable for both p-values and e-values. We prove the theoretical validity of the proposed Domino algorithm and demonstrate through extensive numerical experiments that it consistently achieves rigorous $k$-bFDR control while identifying trustworthy marginal discoveries. Analyses of real data reveal that $k$-bFDR control yields higher-quality rejection sets with greater practical significance.

Problem

• false discovery rate
• boundary FDR
• multiple testing
• arbitrary dependence
• marginal discoveries

Innovation

• k-bFDR
• closure principle
• arbitrary dependence
• Domino framework
• marginal discoveries