Open Access
May 2024 Sequential testing for elicitable functionals via supermartingales
Philippe Casgrain, Martin Larsson, Johanna Ziegel
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Bernoulli 30(2): 1347-1374 (May 2024). DOI: 10.3150/23-BEJ1634


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-ψ tail bound is satisfied.


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Philippe Casgrain. Martin Larsson. Johanna Ziegel. "Sequential testing for elicitable functionals via supermartingales." Bernoulli 30 (2) 1347 - 1374, May 2024.


Received: 1 April 2022; Published: May 2024
First available in Project Euclid: 31 January 2024

MathSciNet: MR4699555
Digital Object Identifier: 10.3150/23-BEJ1634

Keywords: Anytime valid testing , elicitable functionals , identifiable functionals , online optimization , sequential statistics

Vol.30 • No. 2 • May 2024
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