文章基本信息

标题：Optimal Estimators for Threshold-Based Quality Measures
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作者：Aaron Abrams ; Sandy Ganzell ; Henry Landau 等
期刊名称：Journal of Probability and Statistics
印刷版ISSN：1687-952X
电子版ISSN：1687-9538
出版年度：2010
卷号：2010
DOI：10.1155/2010/752750
出版社：Hindawi Publishing Corporation
摘要：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 (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 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 ℝ. By contrast, we give an example showing that, it does not hold for a certain distribution on an infinite tree.