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March, 1985 All Admissible Linear Estimators of a Multivariate Poisson Mean
L. D. Brown, R. H. Farrell
Ann. Statist. 13(1): 282-294 (March, 1985). DOI: 10.1214/aos/1176346593

Abstract

Admissible linear estimators $Mx + \gamma$ must be pointwise limits of Bayes estimators. Using properties of Bayes estimators preserved by taking limits, the structure of $M$ and $\gamma$ can be determined. Among $M, \gamma$ with this structure, a necessary and sufficient condition for admissibility is obtained. This condition is applied to the case of linear (mixture) models. It is shown that only the most trivial such models admit linear estimators of full rank which are admissible or are even limits of Bayes estimators.

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L. D. Brown. R. H. Farrell. "All Admissible Linear Estimators of a Multivariate Poisson Mean." Ann. Statist. 13 (1) 282 - 294, March, 1985. https://doi.org/10.1214/aos/1176346593

Information

Published: March, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0575.62009
MathSciNet: MR773168
Digital Object Identifier: 10.1214/aos/1176346593

Subjects:
Primary: 62C07
Secondary: 62F10

Rights: Copyright © 1985 Institute of Mathematical Statistics

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Vol.13 • No. 1 • March, 1985
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