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.
Publié le : 1980-01-14
Classification:
Common mean,
normal distributions,
estimator,
variance,
62E15,
62F10
@article{1176344904,
author = {Nair, K. Aiyappan},
title = {Variance and Distribution of the Graybill-Deal Estimator of the Common Mean of Two Normal Populations},
journal = {Ann. Statist.},
volume = {8},
number = {1},
year = {1980},
pages = { 212-216},
language = {en},
url = {http://dml.mathdoc.fr/item/1176344904}
}
Nair, K. Aiyappan. Variance and Distribution of the Graybill-Deal Estimator of the Common Mean of Two Normal Populations. Ann. Statist., Tome 8 (1980) no. 1, pp. 212-216. http://gdmltest.u-ga.fr/item/1176344904/