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July, 1973 On Some Properties of Hammersley's Estimator of an Integer Mean
Rasul A. Khan
Ann. Statist. 1(4): 756-762 (July, 1973). DOI: 10.1214/aos/1176342471

Abstract

Let $X_1, \cdots, X_n$ be i.i.d. $N(i, 1), i = 0, \pm 1, \pm 2,\cdots$. Hammersley [2] proposed $\lbrack\bar{X}_n\rbrack$, the nearest integer to the sample mean, as an estimator of $i$. It is proved that $d$ is minimax and admissible relative to zero-one loss. However, it is shown that relative to squared error loss, the estimator is neither admissible nor minimax.

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Rasul A. Khan. "On Some Properties of Hammersley's Estimator of an Integer Mean." Ann. Statist. 1 (4) 756 - 762, July, 1973. https://doi.org/10.1214/aos/1176342471

Information

Published: July, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0263.62003
MathSciNet: MR334350
Digital Object Identifier: 10.1214/aos/1176342471

Subjects:
Primary: 62C15
Secondary: 62F10

Keywords: admissible , Bayes estimator , Bayes risk , discrete normal prior , loss function , minimax

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 4 • July, 1973
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