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arXiv · 2601.11347

Optimal e-values for testing the mean of a bounded random variable against a composite alternative

Sebastian Arnold·Eugenio Clerico
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Abstract

We derive explicitly the e-values with optimal (relative) growth rate in the worst case for testing the mean of a bounded random variable, thereby providing the first application of the (RE)GROW quality criteria beyond the assumption of mutually absolutely continuous hypotheses for e-values originally proposed by Gr\"unwald et al. (2024). For both criteria, we explicitly characterise the alternatives that are most difficult to test against and show that they admit a meaningful interpretation. We give two important examples in which REGROW provides a powerful quality criterion to choose optimal e-variables whereas GROW leads to trivial solutions.

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Sebastian Arnold, Eugenio Clerico. 2026-01-16. Optimal e-values for testing the mean of a bounded random variable against a composite alternative. https://arxiv.org/abs/2601.11347

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