## The Annals of Statistics

### Estimation of Normal Means: Frequentist Estimation of Loss

#### 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.

#### Article information

Source
Ann. Statist. Volume 17, Number 2 (1989), 890-906.

Dates
First available in Project Euclid: 12 April 2007

http://projecteuclid.org/euclid.aos/1176347149

Digital Object Identifier
doi:10.1214/aos/1176347149

Mathematical Reviews number (MathSciNet)
MR994274

Zentralblatt MATH identifier
0714.62003

JSTOR