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Adaptive Maximum Likelihood Estimators of a Location Parameter

Charles J. Stone
The Annals of Statistics
Vol. 3, No. 2 (Mar., 1975), pp. 267-284
Stable URL: http://www.jstor.org/stable/2958945
Page Count: 18
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Adaptive Maximum Likelihood Estimators of a Location Parameter
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Abstract

Consider estimators θ̂n of the location parameter θ based on a sample of size n from θ + X, where the random variable X has an unknown distribution F which is symmetric about the origin but otherwise arbitrary. Let F denote the Fisher information on θ contained in θ + X. We show that there is a nonrandomized translation and scale invariant adaptive maximum likelihood estimator θ̂n of θ which doe not depend on F such that L(n1/2(θ̂n - θ)) → N(0, 1/J) as n → ∞ for all symmetric F.

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