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

TL;DR

This paper introduces a new framework called Domino that controls the generalized boundary false discovery rate (k-bFDR) under arbitrary dependence, enhancing the reliability of marginal discoveries in multiple testing.

Contribution

It proposes the k-bFDR metric, develops the Domino framework based on the closure principle, and proves its validity for controlling error rates under arbitrary dependence.

Findings

Domino guarantees k-bFDR control in simulations.

It identifies more trustworthy discoveries compared to existing methods.

Real data analysis shows improved practical significance of results.

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.