false discovery rate control

Classical false discovery rate (FDR) control methods, such as Benjamini–Hochberg (BH), rely on stringent pointwise control of Type I error (strong control), limiting their applicability under weaker inferential assumptions. This work addresses FDR control when only average-level (i.e., weak) control of significance level is required across tests. Method: We analyze the asymptotic FDR behavior of BH under average-type Type I error constraints and examine the finite-sample validity of the Benjamini–Yekutieli (BY) procedure for dependent p-values. Contribution/Results: We establish, for the first time, the asymptotic FDR control property of BH under weak Type I error control. We further prove that BY correction remains valid for dependent p-values even in finite samples. These results extend FDR theory to nonparametric, high-dimensional sparse, and weak-signal settings—bypassing traditional strong control assumptions—and substantially improve statistical power. The work provides a novel theoretical foundation and practical methodology for multiple testing under weak inference conditions.

This paper addresses the underutilization of heterogeneity and structural information in multiple hypothesis testing by proposing a general e-value–based framework. Methodologically: (1) it introduces a data-dependent weighting scheme—including a leave-one-out heuristic—for flexible aggregation of e-values across subsets, test statistics, and structure-informed covariates; (2) it unifies and extends the Benjamini–Hochberg (BH) and Benjamini–Yekutieli (BY) procedures to accommodate mixed tests and joint group-level–global false discovery rate (FDR) control; (3) it develops a structure-adaptive e-BH procedure that relaxes the independence and homogeneity assumptions inherent in classical p-value–based methods. Theoretically, it guarantees strict finite-sample FDR control. Numerical experiments demonstrate substantial gains in statistical power over state-of-the-art baselines—particularly under heterogeneous, grouped, or covariate-structured settings.

This paper addresses the low statistical power of false discovery rate (FDR) and false coverage rate (FCR) control procedures under arbitrary dependence structures in multiple hypothesis testing. We propose a universal randomization-enhancement strategy based on a single uniform random variable. The method systematically boosts the power of classical procedures—including Benjamini–Yekutieli, e-BH, and Hommel—while preserving exact FDR/FCR control under arbitrary dependence. We provide the first rigorous proof that a single randomization step is never inferior to the original procedure and strictly improves power under any dependence structure; moreover, it unifies and strengthens diverse multiple testing procedures within the e-value framework. Theoretical analysis guarantees strict FDR/FCR control, and extensive simulations confirm substantial power gains. Our core innovation lies in achieving broad-spectrum power enhancement via an extremely simple randomization mechanism, thereby overcoming the long-standing power bottleneck of conventional methods under strong dependence.

Existing e-BH procedures lack order-invariance over e-processes, causing test conclusions to reverse spuriously upon addition of irrelevant data and failing to control the false discovery rate (FDR) — or even the family-wise error rate (FWER) — under arbitrary dependence. This paper provides the first rigorous proof that e-BH violates FDR control in this setting. Method: We propose a novel, order-invariant multiple testing framework built on e-process upper bounds, featuring a dependence-structure-adaptive calibrator. Contribution/Results: Our method guarantees strict FDR control at level α (i.e., FDR-sup ≤ α) for arbitrary dependence structures among hypotheses. It eliminates temporal instability in rejection sets induced by sequential data arrival, ensuring robustness and reproducibility in dynamic data environments. Theoretical guarantees are established without restrictive assumptions on dependence, and the procedure is computationally tractable.

This paper addresses the failure of the stopped e-BH (se-BH) procedure to control the false discovery rate (FDR) under arbitrary stopping times in dependent, data-streaming settings. We identify the root cause as incompatibility between local e-processes and the global filtration, leading to cross-stream information leakage. To resolve this, we introduce verifiable causal conditions—such as absence of unmeasured confounding—and rigorously prove that when e-processes across streams satisfy these conditions, they remain valid e-processes under the global filtration. Consequently, se-BH achieves anytime-valid FDR control for arbitrary stopping times. This is the first online FDR method that simultaneously provides theoretical guarantees and computational feasibility under non-i.i.d., sequentially arriving, and dependent data. The framework enables robust, adaptive multiple testing in real-time applications such as genomics.

This study addresses a critical limitation of traditional multiple testing procedures—such as the Benjamini–Hochberg (BH) method—which control the overall false discovery rate (FDR) but offer no guarantee regarding the reliability of boundary discoveries, i.e., the least significant rejections. The authors propose a novel two-stage adaptive approach: first estimating the number of true null hypotheses using non-significant test statistics, then applying an adjusted threshold within the Support Line (SL) framework to control the error probability of boundary discoveries. This work is the first to integrate adaptivity into boundary FDR control, providing rigorous error guarantees under independence and demonstrating robustness and enhanced power under positive dependence. Theoretical analysis confirms its validity, simulations show substantially improved statistical power over the original SL procedure, and real-world applicability is illustrated through a meta-analysis in psychology.

This work aims to enhance the statistical power of adaptive Benjamini–Hochberg (BH) procedures while maintaining control of the false discovery rate (FDR). By unifying existing adaptive FDR methods under a common framework—interpreting them as weighted BH procedures based on composite e-values (ep-BH)—the study reveals their shared structural foundation and demonstrates for the first time that most estimators of the proportion of true null hypotheses inherently correspond to composite e-values. Building on this insight, the authors propose a novel framework that uniformly improves upon nearly all existing methods without requiring additional assumptions, and they develop a new ep-BH procedure with finite-sample FDR guarantees. In canonical settings such as t-tests, the proposed method achieves consistent and robust power gains while rigorously controlling the FDR.

This work addresses the challenge of controlling the false discovery rate (FDR) under arbitrary dependence structures while enhancing statistical power in online hypothesis testing. The authors propose an online e-closure principle combined with a donation-based composite e-value method, which strictly guarantees FDR control and significantly outperforms existing online multiple testing procedures based on either p-values or e-values. By integrating e-value theory, closure principles, and efficient algorithmic design, the method enables real-time decision-making with a computational complexity of O(log t). Extensive experiments on both synthetic and real-world data demonstrate that the proposed approach achieves superior FDR control accuracy and higher statistical power compared to current state-of-the-art methods.

This study investigates the admissibility and complete class problems for false discovery rate (FDR) control procedures within the e-value framework. Drawing on statistical decision theory, it introduces strong and weak dominance relations to establish, for the first time, a theoretical foundation for admissibility in e-value-based multiple testing with FDR control. The main contributions include proving that every step-down procedure is strongly dominated by some weighted average eBH procedure; demonstrating that weighted average eBH procedures without constant terms are admissible at any FDR level; and showing that, under symmetry, this class of procedures forms a complete class, with its members being maximal only when the FDR threshold is sufficiently small—thereby establishing their structural optimality.

This work addresses a critical limitation in existing multiple testing procedures, which control only the expected false discovery proportion (FDP) and lack high-probability guarantees for the realized FDP, particularly when data-driven thresholds are employed, thereby compromising statistical validity. The authors propose a distribution-free, finite-sample valid framework that constructs a high-probability simultaneous envelope around the empirical distribution function of conformal p-values under the null hypothesis. This approach yields, for the first time, a uniform high-probability upper bound on the FDP that holds simultaneously over all possible rejection thresholds. The method accommodates arbitrary post-hoc threshold selection and allows users to tailor the envelope’s shape to obtain tighter bounds in regions of interest. Empirical evaluations on both synthetic and real-world data demonstrate that the resulting bounds are not only valid but also substantially less conservative than those from existing methods.