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November, 1976 Inadmissibility Results for the Best Invariant Estimator of Two Coordinates of a Location Vector
James O. Berger
Ann. Statist. 4(6): 1065-1076 (November, 1976). DOI: 10.1214/aos/1176343642

Abstract

Let $X = (X_1, X_2, X_3)$ be a random vector with density $f(x - \theta)$, where $\theta = (\theta_1, \theta_2, \theta_3)$ is unknown. It is desired to estimate $(\theta_1, \theta_2)$ using an estimator $(\delta_1(X), \delta_2(X))$, and under a loss function $L(\delta_1 - \theta_1, \delta_2 - \theta_2)$. (Note that $\theta_3$ is a nuisance parameter.) Under certain conditions on $f$ and $L$, it is shown that the best invariant estimator of $(\theta_1, \theta_2)$ is inadmissible.

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James O. Berger. "Inadmissibility Results for the Best Invariant Estimator of Two Coordinates of a Location Vector." Ann. Statist. 4 (6) 1065 - 1076, November, 1976. https://doi.org/10.1214/aos/1176343642

Information

Published: November, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0344.62006
MathSciNet: MR438542
Digital Object Identifier: 10.1214/aos/1176343642

Subjects:
Primary: 62C15
Secondary: 62F10 , 62H99

Keywords: best invariant estimator , inadmissibility , location vector , loss function , risk function

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 6 • November, 1976
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