2022/04/12 by Philippe Casgrain, Martin Larsson, Casgrain, Philippe +3 · 2 citations
Mathematics · Computer Science · Decision Sciences · #Statistical Methods and Inference #Distributed Sensor Networks and Detection Algorithms #Advanced Bandit Algorithms Research
paper · pdf · doi:10.48550/arxiv.2204.05680
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.