Optimal e-values for testing the mean of a bounded random variable against a composite alternative
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917206596517888 |
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| author | Arnold, Sebastian Clerico, Eugenio |
| author_facet | Arnold, Sebastian Clerico, Eugenio |
| contents | 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 Grünwald 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11347 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal e-values for testing the mean of a bounded random variable against a composite alternative Arnold, Sebastian Clerico, Eugenio Statistics Theory 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 Grünwald 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. |
| title | Optimal e-values for testing the mean of a bounded random variable against a composite alternative |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2601.11347 |