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June, 1985 Complete Class Theorems for Estimation of Multivariate Poisson Means and Related Problems
L. D. Brown, R. H. Farrell
Ann. Statist. 13(2): 706-726 (June, 1985). DOI: 10.1214/aos/1176349549

Abstract

Basic decision theory for discrete random variables of the multivariate geometric (power series) type is developed. Some properties of Bayes estimators that carry over in the limit to admissible estimators are obtained. A stepwise generalized Bayes representation of admissible estimators is developed with estimation of the mean of a multivariate Poisson random variable in mind. The development carries over to estimation of the mean of a multivariate negative Binomial random variable. Due to the natural boundary of the parameter space there is an interesting pathology illustrated to some extent by the examples given. Examples include one to show that admissible estimators with somewhere infinite risk do exist in two or more dimensions.

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L. D. Brown. R. H. Farrell. "Complete Class Theorems for Estimation of Multivariate Poisson Means and Related Problems." Ann. Statist. 13 (2) 706 - 726, June, 1985. https://doi.org/10.1214/aos/1176349549

Information

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

zbMATH: 0591.62005
MathSciNet: MR790567
Digital Object Identifier: 10.1214/aos/1176349549

Subjects:
Primary: 62C07
Secondary: 62F10

Keywords: decision theory , estimation , multivariate Poisson parameter

Rights: Copyright © 1985 Institute of Mathematical Statistics

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Vol.13 • No. 2 • June, 1985
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