Dynamic e-closure controls stopped and supremum FDR for growing hypothesis families with continuing evidence, and shows coherent admissible pointwise mergers require one global weight sequence.
Improving online FDR procedures via online analogs of e-closure and compound e-values
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abstract
In many scientific applications, hypotheses are generated and tested continuously in a stream. We develop a framework for improving online multiple testing procedures with false discovery rate (FDR) control under arbitrary dependence. Our approach is two-fold: we construct methods via the online e-closure principle, as well as a novel formulation of online compound e-values that is defined through donations. This yields strict power improvements over state-of-the-art e-value and p-value procedures while retaining FDR control. We further derive algorithms that compute the decision at time $t$ in $O(\log t)$ time, and we demonstrate improved empirical performance on synthetic and real data.
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Dynamic $e$-closure for online hypotheses with any-time-valid evidence: closure principles and projective mergers
Dynamic e-closure controls stopped and supremum FDR for growing hypothesis families with continuing evidence, and shows coherent admissible pointwise mergers require one global weight sequence.