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September, 1987 Admissible Minimax Estimation of a Common Mean of Two Normal Populations
Tatsuya Kubokawa
Ann. Statist. 15(3): 1245-1256 (September, 1987). DOI: 10.1214/aos/1176350503

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.

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Tatsuya Kubokawa. "Admissible Minimax Estimation of a Common Mean of Two Normal Populations." Ann. Statist. 15 (3) 1245 - 1256, September, 1987. https://doi.org/10.1214/aos/1176350503

Information

Published: September, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0658.62036
MathSciNet: MR902256
Digital Object Identifier: 10.1214/aos/1176350503

Subjects:
Primary: 62F10
Secondary: 62C15

Keywords: admissible minimax estimator , Common mean , unbiased estimator

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 3 • September, 1987
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