All admissible linear estimators of a multivariate Poisson mean. (English) Zbl 0575.62009

Brown, L. D.; Farrell, R. H.

Ann. Stat. 13, 282-294 (1985).

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.

MSC:

62C07	Complete class results in statistical decision theory
62H12	Estimation in multivariate analysis
62C15	Admissibility in statistical decision theory
62F10	Point estimation

Keywords:

multivariate Poisson mean; Admissible linear estimators; linear estimators of full rank; limits of Bayes estimators