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May, 1974 Alternative Estimators for the Scale Parameter of the Exponential Distribution with Unknown Location
J. F. Brewster
Ann. Statist. 2(3): 553-557 (May, 1974). DOI: 10.1214/aos/1176342715

Abstract

Let $X_1, X_2,\cdots, X_n$ be independent observations from an exponential distribution with an unknown location-scale parameter $(\mu, \sigma)$. Let $\bar{X} = n^{-1} \sum X_i$ and $M = \min X_i$. Under squared error loss the best location-scale equivariant estimator of $\sigma$ is $\bar{X} - M$, which agrees with the maximum likelihood estimator. Arnold (J. Amer. Statist. Assoc. 65 (1970) 1260-1264) and Zidek (Ann. Statist. 1 (1973) 264-278) have shown that $\bar{X} - M$ is inadmissible but the dominating estimator which they produce is probably inadmissible as well. In this paper a "smoother" dominating procedure is presented, and the risk functions of the various alternatives are plotted. Similar results are obtained for strictly bowl-shaped loss functions.

Citation

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J. F. Brewster. "Alternative Estimators for the Scale Parameter of the Exponential Distribution with Unknown Location." Ann. Statist. 2 (3) 553 - 557, May, 1974. https://doi.org/10.1214/aos/1176342715

Information

Published: May, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0284.62006
MathSciNet: MR359110
Digital Object Identifier: 10.1214/aos/1176342715

Subjects:
Primary: 62C15
Secondary: 62F10

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 3 • May, 1974
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