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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


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.


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K. L. Lu. James O. Berger. "Estimation of Normal Means: Frequentist Estimation of Loss." Ann. Statist. 17 (2) 890 - 906, June, 1989.


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

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

Primary: 62J07
Secondary: 62C10, 62C15

Rights: Copyright © 1989 Institute of Mathematical Statistics


Vol.17 • No. 2 • June, 1989
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