In estimation of a $p$-variate normal mean with identity covariance matrix, Stein-type estimators can offer significant gains over the $\operatorname{mle}$ in terms of risk with respect to sum of squares error loss. Their maximum risk is still equal to $p$, however, which will typically be their "reported loss." In this paper we consider use of data-dependent "loss estimators." Two conditions that are attractive for such a loss estimator are that it be an improved loss estimator under some scoring rule and that it have a type of frequentist validity. Loss estimators with these properties are found for several of the most important Stein-type estimators. One such estimator is a generalized Bayes estimator, and the corresponding loss estimator is its posterior expected loss. Thus Bayesians and frequentists can potentially agree on the analysis of this problem.
Publié le : 1989-06-14
Classification:
Estimated loss,
communication loss,
communication risk,
Stein estimation,
generalized Bayes estimator,
posterior variance,
62J07,
62C10,
62C15
@article{1176347149,
author = {Lu, K. L. and Berger, James O.},
title = {Estimation of Normal Means: Frequentist Estimation of Loss},
journal = {Ann. Statist.},
volume = {17},
number = {1},
year = {1989},
pages = { 890-906},
language = {en},
url = {http://dml.mathdoc.fr/item/1176347149}
}
Lu, K. L.; Berger, James O. Estimation of Normal Means: Frequentist Estimation of Loss. Ann. Statist., Tome 17 (1989) no. 1, pp. 890-906. http://gdmltest.u-ga.fr/item/1176347149/