Optimal Estimators for Threshold-Based Quality Measures

Aaron Abrams, Sandy Ganzell, Henry Landau, Zeph Landau, James Pommersheim and Eric Zaslow

Journal of Probability and Statistics, 2010, vol. 2010, 1-15

Abstract:

We consider a problem in parametric estimation: given samples from an unknown distribution, we want to estimate which distribution, from a given one-parameter family, produced the data. Following Schulman and Vazirani (2005), 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 . 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 . By contrast, we give an example showing that, it does not hold for a certain distribution on an infinite tree.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljps:752750

DOI: 10.1155/2010/752750

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