fdr-controlled change-point selection

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 addresses the growing challenge of change-point detection and localization in independent observation sequences, particularly under complex settings such as nonparametric and heavy-tailed distributions. The authors propose the Lean Bonferroni Detection–False Discovery Rate (LBD-FDR) method, which constructs local neighborhoods and employs an adaptive Bonferroni-type threshold to rigorously control the false discovery rate (FDR) across a broad class of distributional assumptions while effectively identifying change points with sufficient signal strength. Theoretical analysis demonstrates that LBD-FDR achieves the optimal detection constant in Gaussian sequences and, for the first time, establishes strict FDR control in nonparametric and heavy-tailed scenarios. Extensive simulations show that the proposed method outperforms five existing approaches in terms of both detection accuracy and 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.

Classical variance change-point detection methods suffer from p-value bias and inflated Type I error due to data reuse in model selection. Existing post-selection inference (PSI) frameworks are restricted to mean-shift detection and do not extend to variance changes. Method: This paper introduces the first PSI framework for variance change-point detection, proposing two general-purpose constructions for post-selection p-values compatible with diverse algorithms (e.g., piecewise constant modeling) and test forms (e.g., constrained likelihood ratio tests). Leveraging conditional inference, convex optimization, and statistical functional theory, the methods rigorously control Type I error conditional on the selected model path and yield uniformly calibrated p-values. Contribution/Results: We establish theoretical validity of the proposed procedures and demonstrate, via extensive simulations and real-data analyses, their improved statistical power and accurate p-value calibration—overcoming a key limitation of PSI in detecting heteroscedastic structural changes.

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 work proposes a Posterior Conformal Selection (PH-CS) framework that overcomes the rigidity of traditional conformal selection methods, which require a pre-specified false discovery rate (FDR) threshold and thus struggle to balance selection size against FDR control. PH-CS eliminates the need for any preset FDR level by constructing a path of candidate selection sets and estimating their data-driven false discovery proportions (FDPs). Leveraging conformal e-values together with the e-BH procedure, the framework enables users to dynamically choose an optimal operating point based on a custom utility function. The method provides reliable average-case FDP estimates under finite samples, extends naturally to general risk control, and demonstrates competitive FDR control performance while accurately estimating FDP and satisfying utility constraints in both synthetic and real-data experiments.

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 the challenge of accurately attributing detected change points in multivariate time series to specific subsets of variables. The authors propose a post-hoc, nonparametric testing framework that, after an offline change point has been identified, determines whether the change occurs in one of two pre-specified coordinate blocks or in both. Built upon two-sample nonparametric hypothesis testing, the method offers rigorous theoretical guarantees for Type I error control. Empirical evaluations on both synthetic and real-world datasets demonstrate that the proposed approach achieves high attribution accuracy and strong robustness in identifying the components responsible for the change.

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 study addresses the problem of determining whether high-frequency monitoring data return to their pre-intervention baseline distribution following an intervention. The authors propose a sequential testing procedure that requires no assumptions about the underlying data distribution. The method constructs a discrepancy measure via universal inference and combines it with individualized empirical calibration to form a non-negative supermartingale, yielding an e-process that enables valid detection of the recovery time at any arbitrary stopping point without specifying a null model. Theoretical analysis provides finite-sample bounds on the calibration error, and both simulations and a clinical case study demonstrate the method’s superior performance in accurately identifying the time at which baseline conditions are restored.