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Bringing Closure to False Discovery Rate Control: A General Principle for Multiple Testing
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We present a novel necessary and sufficient principle for multiple testing methods controlling an expected loss. This principle asserts that every such multiple testing method is a special case of a general closed testing procedure based on e-values. It generalizes the Closure Principle, known to underlie all methods controlling familywise error and tail probabilities of false discovery proportions, to a large class of error rates -- in particular to the false discovery rate (FDR). By writing existing methods as special cases of this procedure, we can achieve uniform improvements, as we demonstrate for the e-Benjamini-Hochberg and the Benjamini-Yekutieli procedures, and the self-consistent method of Su (2018). We also show that methods derived using our novel e-Closure Principle generally control their error rate not just for one rejected set, but simultaneously over many, allowing post hoc flexibility for the researcher. Moreover, because all multiple testing methods for the expected loss error metrics covered by our framework are derived from the same procedure, researchers may even choose the error metric post hoc. Under certain conditions, this flexibility even extends to post hoc choice of the nominal error rate.
Forward citations
Cited by 8 Pith papers
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Closed BH improves the Benjamini-Hochberg procedure via e-Closure, controlling FDR under PRDS or weaker assumptions while never rejecting fewer hypotheses.
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Post-hoc conformal selection creates a path of selection sets with estimated false discovery proportions, enabling data-driven adaptive FDR control with average reliability guarantees via e-variables and e-BH.
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Demonstrates formal equivalence between adaptive design tools and e-value sequential tests while noting differences in emphasis on flexibility aspects.
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Generalized Boundary FDR Control under Arbitrary Dependence: An Approach on Closure Principle
Domino guarantees k-bFDR control under arbitrary dependence via the closure principle, extending boundary FDR methods to general settings for both p-values and e-values.
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Beyond Fixed False Discovery Rates: Post-Hoc Conformal Selection with E-Variables
PH-CS produces a path of conformal selection sets with finite-sample post-hoc FDP estimates so users can maximize a utility balancing selection size and FDR after seeing data.
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Active Hypothesis Testing under Computational Budgets with Applications to GWAS and LLM
Active hypothesis testing framework uses auxiliary statistics for data-adaptive budget allocation to produce valid p-values or e-values with optimality under independence and admissibility under dependence.
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