For a normally distributed mixed model with two unknown variance components $\theta_1$ and $\theta_2$, a tractable characterization is given for the admissible estimators within the class $\tilde{\mathscr{N}}_\delta$ of invariant quadratic unbiased estimators for $\delta_1\theta_1 + \delta_2\theta_2$. Here the term admissible is used with reference only to the class $\tilde{\mathscr{N}}_\delta$. This characterization is based on a result for general linear models which characterizes the admissible estimators within the class of linear unbiased estimators. The admissibility of MINQUE estimators and the usual analysis of variance estimators is considered.
Publié le : 1976-09-14
Classification:
Variance components,
quadratic estimators,
admissibility,
complete class,
Henderson method III,
MINQUE,
62J99,
62C15
@article{1176343586,
author = {Olsen, Anthony and Seely, Justus and Birkes, David},
title = {Invariant Quadratic Unbiased Estimation for Two Variance Components},
journal = {Ann. Statist.},
volume = {4},
number = {1},
year = {1976},
pages = { 878-890},
language = {en},
url = {http://dml.mathdoc.fr/item/1176343586}
}
Olsen, Anthony; Seely, Justus; Birkes, David. Invariant Quadratic Unbiased Estimation for Two Variance Components. Ann. Statist., Tome 4 (1976) no. 1, pp. 878-890. http://gdmltest.u-ga.fr/item/1176343586/