In the paper an explicit expression for the Bayes invariant quadratic unbiased estimate of the linear function of the variance components is presented for the mixed linear model $\bold{t=X\beta+\epsilon}$, $\bold{E(t)=X\beta}$, $\bold{D(t)=0_1U_1+0_2U_2}$ with the unknown variance componets in the normal case. The matrices $\bold{U_1}$, $\bold{U_2}$ may be singular. Applications to two examples of the analysis of variance are given.
@article{104241,
author = {Jaroslav Stuchl\'y},
title = {Bayes unbiased estimation in a model with two variance components},
journal = {Applications of Mathematics},
volume = {32},
year = {1987},
pages = {120-130},
zbl = {0625.62019},
mrnumber = {0885759},
language = {en},
url = {http://dml.mathdoc.fr/item/104241}
}
Stuchlý, Jaroslav. Bayes unbiased estimation in a model with two variance components. Applications of Mathematics, Tome 32 (1987) pp. 120-130. http://gdmltest.u-ga.fr/item/104241/
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