An information-theoretic lower bound in time-uniform estimation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916283320107008 |
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| author | Duchi, John C. Haque, Saminul |
| author_facet | Duchi, John C. Haque, Saminul |
| contents | We present an information-theoretic lower bound for the problem of parameter estimation with time-uniform coverage guarantees. Via a new a reduction to sequential testing, we obtain stronger lower bounds that capture the hardness of the time-uniform setting. In the case of location model estimation, logistic regression, and exponential family models, our $Ω(\sqrt{n^{-1}\log \log n})$ lower bound is sharp to within constant factors in typical settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08794 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An information-theoretic lower bound in time-uniform estimation Duchi, John C. Haque, Saminul Information Theory Statistics Theory We present an information-theoretic lower bound for the problem of parameter estimation with time-uniform coverage guarantees. Via a new a reduction to sequential testing, we obtain stronger lower bounds that capture the hardness of the time-uniform setting. In the case of location model estimation, logistic regression, and exponential family models, our $Ω(\sqrt{n^{-1}\log \log n})$ lower bound is sharp to within constant factors in typical settings. |
| title | An information-theoretic lower bound in time-uniform estimation |
| topic | Information Theory Statistics Theory |
| url | https://arxiv.org/abs/2402.08794 |