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| Hauptverfasser: | , , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2507.08811 |
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| _version_ | 1866908447130255360 |
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| author | Abrams, Aaron Ganzell, Sandy Landau, Henry Landau, Zeph Pommersheim, James Zaslow, Eric |
| author_facet | Abrams, Aaron Ganzell, Sandy Landau, Henry Landau, Zeph Pommersheim, James Zaslow, Eric |
| contents | We consider a problem in parametric estimation: given $n$ samples from an unknown distribution, we want to estimate which distribution, from a given one-parameter family, produced the data. Following Schulman and Vazirani, we evaluate an estimator in terms of the chance of being within a specified tolerance of the correct answer, in the worst case. We provide optimal estimators for several families of distributions on $\mathbb{R}$. We prove that for distributions on a compact space, there is always an optimal estimator that is translation-invariant, and we conjecture that this conclusion also holds for any distribution on $\mathbb{R}$. By contrast, we give an example showing it does not hold for a certain distribution on an infinite tree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08811 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal estimators for threshold-based quality measures Abrams, Aaron Ganzell, Sandy Landau, Henry Landau, Zeph Pommersheim, James Zaslow, Eric Statistics Theory Probability We consider a problem in parametric estimation: given $n$ samples from an unknown distribution, we want to estimate which distribution, from a given one-parameter family, produced the data. Following Schulman and Vazirani, we evaluate an estimator in terms of the chance of being within a specified tolerance of the correct answer, in the worst case. We provide optimal estimators for several families of distributions on $\mathbb{R}$. We prove that for distributions on a compact space, there is always an optimal estimator that is translation-invariant, and we conjecture that this conclusion also holds for any distribution on $\mathbb{R}$. By contrast, we give an example showing it does not hold for a certain distribution on an infinite tree. |
| title | Optimal estimators for threshold-based quality measures |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2507.08811 |