## The Annals of Statistics

- Ann. Statist.
- Volume 15, Number 3 (1987), 1245-1256.

### Admissible Minimax Estimation of a Common Mean of Two Normal Populations

#### Abstract

Consider the problem of estimating the common mean $\mu$ of two normal populations with unknown variances $\sigma^2_1$ and $\sigma^2_2$ under the quadratic loss $(\hat{\mu} - \mu)^2/\sigma^2_1$. A family of minimax estimators with smaller risk than the sample mean in the first population is given, out of which admissible minimax estimators are developed. A class of better estimators of $\mu$ under squared-error loss, which is wider than found by Bhattacharya, is obtained.

#### Article information

**Source**

Ann. Statist., Volume 15, Number 3 (1987), 1245-1256.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176350503

**Digital Object Identifier**

doi:10.1214/aos/1176350503

**Mathematical Reviews number (MathSciNet)**

MR902256

**Zentralblatt MATH identifier**

0658.62036

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62F10: Point estimation

Secondary: 62C15: Admissibility

**Keywords**

Common mean admissible minimax estimator unbiased estimator

#### Citation

Kubokawa, Tatsuya. Admissible Minimax Estimation of a Common Mean of Two Normal Populations. Ann. Statist. 15 (1987), no. 3, 1245--1256. doi:10.1214/aos/1176350503. https://projecteuclid.org/euclid.aos/1176350503