## The Annals of Statistics

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

Tatsuya Kubokawa

#### 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

#### 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