Optimal e-values for testing the mean of a bounded random variable against a composite alternative
Statistics Theory
2026-01-19 v1 Statistics Theory
Abstract
We derive the unique e-values with optimal (relative) growth rate in the worst case for testing the mean of a bounded random variable, hereby contributing with the first application beyond the assumption of mutually absolutely continuous hypotheses of the (RE)GROW quality criteria for e-values originally proposed by Gr\"unwald et al. (2024). For both criteria, we characterise explicitly the alternatives for which it is most difficult to test against, which also admit a meaningful interpretation. We give two important examples of interest where REGROW provides a powerful quality criterion to choose optimal e-variables whereas GROW leads to trivial solutions.
Cite
@article{arxiv.2601.11347,
title = {Optimal e-values for testing the mean of a bounded random variable against a composite alternative},
author = {Sebastian Arnold and Eugenio Clerico},
journal= {arXiv preprint arXiv:2601.11347},
year = {2026}
}