# Article

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Keywords:
risk function; explicit expression; Bayes invariant quadratic unbiased estimate; linear function of the variance components; mixed linar model; normal case
Summary:
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.
References:
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