The problem of estimating a $p$-variate normal mean under arbitrary quadratic loss when $p \geq 3$ is considered. Any estimator having uniformly smaller risk than the maximum likelihood estimator $\delta^0$ will have significantly smaller risk only in a fairly small region of the parameter space. A relatively simple minimax estimator is developed which allows the user to select the region in which significant improvement over $\delta^0$ is to be achieved. Since the desired region of improvement should probably be chosen to coincide with prior beliefs concerning the whereabouts of the normal mean, the estimator is also analyzed from a Bayesian viewpoint.
Publié le : 1982-03-14
Classification:
Minimax,
normal mean,
quadratic loss,
risk function,
prior information,
Bayes risk,
62C99,
62F15,
62F10,
62H99
@article{1176345691,
author = {Berger, James O.},
title = {Selecting a Minimax Estimator of a Multivariate Normal Mean},
journal = {Ann. Statist.},
volume = {10},
number = {1},
year = {1982},
pages = { 81-92},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345691}
}
Berger, James O. Selecting a Minimax Estimator of a Multivariate Normal Mean. Ann. Statist., Tome 10 (1982) no. 1, pp. 81-92. http://gdmltest.u-ga.fr/item/1176345691/