BOOST is the power-optimal strong-FWER procedure for block size three, delivering linear-cost validity and 1.4-1.7x power gains over baselines via KKT allocation and a sample-split plug-in.
arXiv preprint arXiv:2501.09015 , year=
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abstract
The closure principle is a standard tool for achieving strong family-wise error rate (FWER) control in multiple testing problems. We develop an e-value-based closed testing framework that inherits nice properties of e-values, which are common in settings of sequential hypothesis testing or universal inference for irregular parametric models. We prove that e-value-based closed testing strongly controls the post-hoc FWER in the static setting, and has stronger anytime-valid and always-valid FWER-controlling properties in the sequential setting. Furthermore, we extend the celebrated graphical approach for FWER control (Bretz et al. 2009), using the weighted average of e-values for the local test, a strictly more powerful approach than weighted Bonferroni local tests with inverse e-values as p-values. In general, the computational cost for closed testing can be exponential in the number of hypotheses. Although the computational shortcuts for the p-value-based graphical approach are not applicable, we develop an efficient polynomial-time algorithm using dynamic programming for e-value-based graphical approaches with any directed acyclic graph, and tailored algorithms for the e-Holm procedure previously studied by Vovk and Wang (2021) and the e-Fallback procedure.
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E-measures generalize E-values to intersection-closed hypothesis classes, yielding uniform evidence bounds, automatic familywise evidence control without multiplicity correction, and a frequentist E-prior to E-posterior update.
Demonstrates formal equivalence between adaptive design tools and e-value sequential tests while noting differences in emphasis on flexibility aspects.
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.
The weighted Holm procedure (WHP) based on ordered weighted p-values is uniformly more powerful than the weighted alternative Holm procedure (WAP) based on ordered raw p-values, with stronger optimality properties under FWER control.
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