## The Annals of Statistics

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

Khursheed Alam

#### 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

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