## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 41, Number 2 (1970), 642-645.

### A Family of Minimax Estimators of the Mean of a Multivariate Normal Distribution

#### Abstract

A family of estimators, each of which dominates the "usual" one, is given for the problem of simultaneously estimating means of three or more independent normal random variables which have a common unknown variance. Charles Stein [4] established the existence of such estimators (for the case of a known variance) and later, with James [3], exhibited some, both for the case of unknown common variances considered here and for other cases as well. Alam and Thompson [1] have also obtained estimators which dominate the usual one. The class of estimators given in this paper contains those of James and Stein and also those of Alam and Thompson.

#### Article information

**Source**

Ann. Math. Statist., Volume 41, Number 2 (1970), 642-645.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177697104

**Digital Object Identifier**

doi:10.1214/aoms/1177697104

**Mathematical Reviews number (MathSciNet)**

MR253461

**JSTOR**

links.jstor.org

#### Citation

Baranchik, A. J. A Family of Minimax Estimators of the Mean of a Multivariate Normal Distribution. Ann. Math. Statist. 41 (1970), no. 2, 642--645. doi:10.1214/aoms/1177697104. https://projecteuclid.org/euclid.aoms/1177697104