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January, 1980 Variance and Distribution of the Graybill-Deal Estimator of the Common Mean of Two Normal Populations
K. Aiyappan Nair
Ann. Statist. 8(1): 212-216 (January, 1980). DOI: 10.1214/aos/1176344904

Abstract

Let $x$ and $y$ be two independent normal variables with mean $\mu$ and variances $\sigma^2_1$ and $\sigma^2_2$ respectively. Also let $S^2_1$ and $S^2_2$ be two independent estimators of $\sigma^2_1$ and $\sigma^2_2$ such that $mS^2_1\sigma^{-2}_1$ and $nS^2_2\sigma^{-2}_2$ are chi-squares with $m$ and $n$ degrees of freedom respectively. The Graybill-Deal estimator of $\mu$ is $\hat{\mu} = (S^{-2}_1x + S^{-2}_2y)/(S^{-2}_1 + S^{-2}_2)$. In this paper an expression for the variance of $\hat{\mu}$ is given. Also bounds for the distribution of $\hat{\mu}$ are studied.

Citation

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K. Aiyappan Nair. "Variance and Distribution of the Graybill-Deal Estimator of the Common Mean of Two Normal Populations." Ann. Statist. 8 (1) 212 - 216, January, 1980. https://doi.org/10.1214/aos/1176344904

Information

Published: January, 1980
First available in Project Euclid: 12 April 2007

zbMATH: 0422.62015
MathSciNet: MR557567
Digital Object Identifier: 10.1214/aos/1176344904

Subjects:
Primary: 62E15
Secondary: 62F10

Keywords: Common mean , estimator , normal distributions , variance

Rights: Copyright © 1980 Institute of Mathematical Statistics

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Vol.8 • No. 1 • January, 1980
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