## The Annals of Statistics

- Ann. Statist.
- Volume 1, Number 3 (1973), 517-525.

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

#### Abstract

Let the $p$-component vector $X$ be normally distributed with mean $\xi$ and covariance $\sigma^2I$ where $I$ denotes the identity matrix and $\sigma$ is known. For estimating $\xi$ with quadratic loss, it is known that $X$ is minimax but inadmissible for $p \geqq 3$. We obtain a family of estimators which dominate $X$ and are admissible. These estimators are, therefore, both minimax and admissible.

#### Article information

**Source**

Ann. Statist., Volume 1, Number 3 (1973), 517-525.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176342417

**Digital Object Identifier**

doi:10.1214/aos/1176342417

**Mathematical Reviews number (MathSciNet)**

MR353524

**Zentralblatt MATH identifier**

0259.62007

**JSTOR**

links.jstor.org

#### Citation

Alam, Khursheed. A Family of Admissible Minimax Estimators of the Mean of a Multivariate Normal Distribution. Ann. Statist. 1 (1973), no. 3, 517--525. doi:10.1214/aos/1176342417. https://projecteuclid.org/euclid.aos/1176342417