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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.17554 |
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| _version_ | 1866915080535277568 |
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| author | Grünwald, Peter Hao, Yunda Balsubramani, Akshay |
| author_facet | Grünwald, Peter Hao, Yunda Balsubramani, Akshay |
| contents | We consider growth-optimal e-variables with maximal e-power, both in an absolute and relative sense, for simple null hypotheses for a $d$-dimensional random vector, and multivariate composite alternatives represented as a set of $d$-dimensional means $\meanspace_1$. These include, among others, the set of all distributions with mean in $\meanspace_1$, and the exponential family generated by the null restricted to means in $\meanspace_1$. We show how these optimal e-variables are related to Csiszár-Sanov-Chernoff bounds, first for the case that $\meanspace_1$ is convex (these results are not new; we merely reformulate them) and then for the case that $\meanspace_1$ `surrounds' the null hypothesis (these results are new). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17554 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Growth-Optimal E-Variables and an extension to the multivariate Csiszár-Sanov-Chernoff Theorem Grünwald, Peter Hao, Yunda Balsubramani, Akshay Information Theory Statistics Theory We consider growth-optimal e-variables with maximal e-power, both in an absolute and relative sense, for simple null hypotheses for a $d$-dimensional random vector, and multivariate composite alternatives represented as a set of $d$-dimensional means $\meanspace_1$. These include, among others, the set of all distributions with mean in $\meanspace_1$, and the exponential family generated by the null restricted to means in $\meanspace_1$. We show how these optimal e-variables are related to Csiszár-Sanov-Chernoff bounds, first for the case that $\meanspace_1$ is convex (these results are not new; we merely reformulate them) and then for the case that $\meanspace_1$ `surrounds' the null hypothesis (these results are new). |
| title | Growth-Optimal E-Variables and an extension to the multivariate Csiszár-Sanov-Chernoff Theorem |
| topic | Information Theory Statistics Theory |
| url | https://arxiv.org/abs/2412.17554 |