## The Annals of Statistics

### All Admissible Linear Estimators of a Multivariate Poisson Mean

#### 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.

#### Article information

Source
Ann. Statist., Volume 13, Number 1 (1985), 282-294.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176346593

Digital Object Identifier
doi:10.1214/aos/1176346593

Mathematical Reviews number (MathSciNet)
MR773168

Zentralblatt MATH identifier
0575.62009

JSTOR