finite-null fdr 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 work addresses the challenge of controlling the false discovery rate (FDR) in large-scale multiple hypothesis testing when only a limited number of null samples are available and hypotheses exhibit arbitrary structural dependencies. The authors propose a unified framework that leverages reproducing kernel Hilbert spaces (RKHS) to model the intrinsic structure among hypotheses, integrates uncertainty quantification of finite-sample p-values, and extends mirror statistics to the counting space. Within this framework, they construct two decision rules that provide rigorous FDR guarantees. Their approach is the first to simultaneously handle data scarcity and complex dependency structures, achieving substantially improved statistical power while maintaining robustness. Additionally, it offers an efficient strategy for allocating scarce null-distribution samples, enabling a flexible trade-off between precision and power in structured multiple testing.

This paper investigates the false discovery rate (FDR) control performance of the Benjamini–Hochberg (BH) procedure under *composite p-values*—i.e., p-values that are only required to be super-uniform on all true null hypotheses, a weaker condition than standard uniformity. Theoretical analysis establishes that, under independence, FDR ≤ 1.93α; when all nulls are true, FDR ≤ α + 2α²; and under positive dependence, FDR may inflate by a factor of O(log m), with matching tight upper and lower bound constructions. This work provides the first systematic characterization of the robustness boundary of the BH procedure to composite p-values, precisely delineating its FDR control capability—and inherent limitations—when the classical uniformity assumption is relaxed. The results establish a new theoretical foundation for multiple testing in high-dimensional settings with complex dependencies, enhancing both flexibility and statistical power.

This paper addresses the low statistical power and poor resolution of conventional placebo tests in synthetic control method (SCM) causal inference under small-sample settings—particularly when α = 0.05 and the number of donor units *N* is small. We propose a leave-two-out randomization inference framework that rigorously controls Type I error rates in finite samples while substantially improving test resolution and statistical power, even under stringent significance levels (α < 1/*N*). Unlike permutation or rank-based tests, our framework accommodates non-uniform treatment assignment and integrates formal sensitivity analysis for robust causal inference. Empirical results demonstrate that, under moderate effect sizes, the proposed method achieves lower actual Type I error rates and higher statistical power compared to standard approaches.

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.

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.

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.

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 the problem of multiple hypothesis testing for edge distributions across multiple data streams. It proposes a sequential testing procedure that, for the first time, systematically incorporates arbitrary forms of prior information about the configuration of true and false hypotheses—such as known values or lower bounds on the number of active streams under each hypothesis, or mutual exclusivity constraints—while rigorously controlling the familywise error rate. By integrating sequential analysis with a search strategy over minimal alternative hypothesis configurations, the method achieves asymptotic optimality in terms of expected sample size among all valid procedures, without compromising reliability. Theoretical analysis establishes its computational efficiency and asymptotic optimality, and numerical experiments further demonstrate its substantial advantages in both testing efficiency and accuracy.