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necessary and sufficient conditions for an existence; Bayes invariant quadratic unbiased estimate; linear function of variance components; mixed linear model; three unknown variance components; normal case
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.
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