Translator Disclaimer
June, 1989 Estimation of Normal Means: Frequentist Estimation of Loss
K. L. Lu, James O. Berger
Ann. Statist. 17(2): 890-906 (June, 1989). DOI: 10.1214/aos/1176347149

Abstract

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.

Citation

Download Citation

K. L. Lu. James O. Berger. "Estimation of Normal Means: Frequentist Estimation of Loss." Ann. Statist. 17 (2) 890 - 906, June, 1989. https://doi.org/10.1214/aos/1176347149

Information

Published: June, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0714.62003
MathSciNet: MR994274
Digital Object Identifier: 10.1214/aos/1176347149

Subjects:
Primary: 62J07
Secondary: 62C10, 62C15

Rights: Copyright © 1989 Institute of Mathematical Statistics

JOURNAL ARTICLE
17 PAGES


SHARE
Vol.17 • No. 2 • June, 1989
Back to Top