The problem of estimating several normal mean vectors in an empirical Bayes situation is considered. In this case, it reduces to the problem of estimating the inverse of a covariance matrix in the standard multivariate normal situation using a particular loss function. Estimators which dominate any constant multiple of the inverse sample covariance matrix are presented. These estimators work by shrinking the sample eigenvalues toward a central value, in much the same way as the James-Stein estimator for a mean vector shrinks the maximum likelihood estimators toward a common value. These covariance estimators then lead to a class of multivariate estimators of the mean, each of which dominates the maximum likelihood estimator.
Publié le : 1976-01-14
Classification:
Multivariate empirical Bayes,
Stein's estimator,
minimax estimation,
mean of a multivariate normal distribution,
estimating a covariance matrix,
James-Stein estimator,
simultaneous estimation,
combining estimates,
62F10,
62C99
@article{1176343345,
author = {Efron, Bradley and Morris, Carl},
title = {Multivariate Empirical Bayes and Estimation of Covariance Matrices},
journal = {Ann. Statist.},
volume = {4},
number = {1},
year = {1976},
pages = { 22-32},
language = {en},
url = {http://dml.mathdoc.fr/item/1176343345}
}
Efron, Bradley; Morris, Carl. Multivariate Empirical Bayes and Estimation of Covariance Matrices. Ann. Statist., Tome 4 (1976) no. 1, pp. 22-32. http://gdmltest.u-ga.fr/item/1176343345/