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.
Publié le : 1985-03-14
Classification:
Estimation,
multivariate Poisson parameter,
decision theory,
linear estimators,
admissibility,
linear models,
62C07,
62F10
@article{1176346593,
author = {Brown, L. D. and Farrell, R. H.},
title = {All Admissible Linear Estimators of a Multivariate Poisson Mean},
journal = {Ann. Statist.},
volume = {13},
number = {1},
year = {1985},
pages = { 282-294},
language = {en},
url = {http://dml.mathdoc.fr/item/1176346593}
}
Brown, L. D.; Farrell, R. H. All Admissible Linear Estimators of a Multivariate Poisson Mean. Ann. Statist., Tome 13 (1985) no. 1, pp. 282-294. http://gdmltest.u-ga.fr/item/1176346593/