In the paper necessary and sufficient conditions for the existence and an explicit expression for the Bayes invariant quadratic unbiased estimate of the linear function of the variance components are presented for the mixed linear model $\bold{t=X\beta + \epsilon}$, $\bold{E(t)=X\beta}$, $\bold {Var(t)=0_1U_1 + 0_2U_2 + 0_3U_3}$, with three unknown variance components in the normal case. An application to some examples from the analysis of variance is given.
@article{104365,
author = {Jaroslav Stuchl\'y},
title = {Bayes unbiased estimation in a model with three variance components},
journal = {Applications of Mathematics},
volume = {34},
year = {1989},
pages = {375-386},
zbl = {0689.62026},
mrnumber = {1014078},
language = {en},
url = {http://dml.mathdoc.fr/item/104365}
}
Stuchlý, Jaroslav. Bayes unbiased estimation in a model with three variance components. Applications of Mathematics, Tome 34 (1989) pp. 375-386. http://gdmltest.u-ga.fr/item/104365/
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