Date of this Version
Annals of Statistics
Admissible linear estimators Mx+γ must be pointwise limits of Bayes estimators. Using properties of Bayes estimators preserved by taking limits, the structure of M and γ can be determined. Among M,γ 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.
estimation, multivariate Poisson parameter, decision theory, linear estimators, admissibility, linear models
Brown, L. D., & Farrell, R. H. (1985). All Admissible Linear Estimators of a Multivariate Poisson Mean. Annals of Statistics, 13 (1), 282-294. http://dx.doi.org/10.1214/aos/1176346593
Date Posted: 27 November 2017
This document has been peer reviewed.