Mathematics > Statistics Theory
[Submitted on 12 Apr 2022 (v1), last revised 4 Jun 2023 (this version, v2)]
Title:Anytime-valid sequential testing for elicitable functionals via supermartingales
View PDFAbstract:We design sequential tests for a large class of nonparametric null hypotheses based on elicitable and identifiable functionals. Such functionals are defined in terms of scoring functions and identification functions, which are ideal building blocks for constructing nonnegative supermartingales under the null. This in turn yields sequential tests via Ville's inequality. Using regret bounds from Online Convex Optimization, we obtain rigorous guarantees on the asymptotic power of the tests for a wide range of alternative hypotheses. Our results allow for bounded and unbounded data distributions, assuming that a sub-$\psi$ tail bound is satisfied.
Submission history
From: Philippe Casgrain [view email][v1] Tue, 12 Apr 2022 10:20:09 UTC (354 KB)
[v2] Sun, 4 Jun 2023 19:28:30 UTC (2,453 KB)
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