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arXiv · 2507.08811

Optimal estimators for threshold-based quality measures

Aaron Abrams·Sandy Ganzell·Henry Landau·Zeph Landau·James Pommersheim·Eric Zaslow
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Abstract

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.

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Aaron Abrams, Sandy Ganzell, Henry Landau, Zeph Landau, James Pommersheim, Eric Zaslow. 2025-06-26. Optimal estimators for threshold-based quality measures. https://arxiv.org/abs/2507.08811

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