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March, 1975 Adaptive Maximum Likelihood Estimators of a Location Parameter
Charles J. Stone
Ann. Statist. 3(2): 267-284 (March, 1975). DOI: 10.1214/aos/1176343056

Abstract

Consider estimators $\hat{\theta}_n$ of the location parameter $\theta$ based on a sample of size $n$ from $\theta + X$, where the random variable $X$ has an unknown distribution $F$ which is symmetric about the origin but otherwise arbitrary. Let $\mathscr{F}$ denote the Fisher information on $\theta$ contained in $\theta + X$. We show that there is a nonrandomized translation and scale invariant adaptive maximum likelihood estimator $\hat{\theta}_n$ of $\theta$ which doe not depend on $F$ such that $\mathscr{L}(n^{\frac{1}{2}}(\hat{\theta}_n - \theta)) \rightarrow N(0, 1/\mathscr{J})$ as $n \rightarrow \infty$ for all symmetric $F$.

Citation

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Charles J. Stone. "Adaptive Maximum Likelihood Estimators of a Location Parameter." Ann. Statist. 3 (2) 267 - 284, March, 1975. https://doi.org/10.1214/aos/1176343056

Information

Published: March, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0303.62026
MathSciNet: MR362669
Digital Object Identifier: 10.1214/aos/1176343056

Subjects:
Primary: 62F10
Secondary: 62G35

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 2 • March, 1975
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