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March, 1976 Admissibility Results for Generalized Bayes Estimators of Coordinates of a Location Vector
James O. Berger
Ann. Statist. 4(2): 334-356 (March, 1976). DOI: 10.1214/aos/1176343410

Abstract

Let $X$ be an $n$-dimensional random vector with density $f(x - \theta)$. It is desired to estimate $\theta_1$, under a strictly convex loss $L(\delta - \theta_1)$. If $F$ is a generalized Bayes prior density, the admissibility of the corresponding generalized Bayes estimator, $\delta_F$, is considered. An asymptotic approximation to $\delta_F$ is found. Using this approximation, it is shown that if (i) $f$ has enough moments, (ii) $L$ and $F$ are smooth enough, and (iii) $F(\theta) \leqq K(|\theta_1| + \sum^n_{i=2} \theta_i^2)^{(3-n)/2}$, then $\delta_F$ is admissible for estimating $\theta_1$. For example, assume that $F(\theta) \equiv 1$ and that $L$ is squared error loss. Under appropriate conditions it can be shown that $\delta_F(x) = x_1$, and that $\delta_F$ is the best invariant estimator. If, in addition, $f$ has 7 absolute moments and $n \leqq 3$, it can be concluded that $\delta_F$ is admissible.

Citation

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James O. Berger. "Admissibility Results for Generalized Bayes Estimators of Coordinates of a Location Vector." Ann. Statist. 4 (2) 334 - 356, March, 1976. https://doi.org/10.1214/aos/1176343410

Information

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

zbMATH: 0323.62005
MathSciNet: MR400486
Digital Object Identifier: 10.1214/aos/1176343410

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

Keywords: Admissibility , generalized Bayes estimators , location vector

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 2 • March, 1976
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