This note extends a result of Efron and Morris on domination of the maximum likelihood estimator for the mean of a multivariate normal distribution. We show that this result and our extension follow from a certain differential inequality. In a certain class of estimators having a unique unbiased estimator for the quadratic risk we find necessary and sufficient conditions for risk estimate dominance of a particular set of estimators. We show that, in the sense of risk estimates, these conditions imply that there are no estimators in this class which dominate the James-Stein or truncated James-Stein estimators.
Publié le : 1978-07-14
Classification:
James-Stein estimator,
truncated James-Stein estimator,
mean of a multivariate normal distribution,
unbiased estimator of the risk,
risk estimate dominance,
62F10,
62C99
@article{1176344265,
author = {Moore, Terry and Brook, Richard J.},
title = {Risk Estimate Optimality of James-Stein Estimators},
journal = {Ann. Statist.},
volume = {6},
number = {1},
year = {1978},
pages = { 917-919},
language = {en},
url = {http://dml.mathdoc.fr/item/1176344265}
}
Moore, Terry; Brook, Richard J. Risk Estimate Optimality of James-Stein Estimators. Ann. Statist., Tome 6 (1978) no. 1, pp. 917-919. http://gdmltest.u-ga.fr/item/1176344265/