The Annals of Statistics

Complete Class Theorems for Estimation of Multivariate Poisson Means and Related Problems

L. D. Brown and R. H. Farrell

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 13, Number 2 (1985), 706-726.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349549

Digital Object Identifier
doi:10.1214/aos/1176349549

Mathematical Reviews number (MathSciNet)
MR790567

Zentralblatt MATH identifier
0591.62005

JSTOR
links.jstor.org

Subjects
Primary: 62C07: Complete class results
Secondary: 62F10: Point estimation

Keywords
Estimation multivariate Poisson parameter decision theory

Citation

Brown, L. D.; Farrell, R. H. Complete Class Theorems for Estimation of Multivariate Poisson Means and Related Problems. Ann. Statist. 13 (1985), no. 2, 706--726. doi:10.1214/aos/1176349549. https://projecteuclid.org/euclid.aos/1176349549


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