The Bayes estimator of the variance components and its admissibility

Jaroslav Stuchlý

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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 $𝐭 = 𝐗 β + ϵ$ , $𝐄 (𝐭) = 𝐗 β$ , $𝐃 (𝐭) = 0_{1} 𝐔_{1} + 0_{2} 𝐔_{2}$ with the unknown variance componets in the normal case. The matrices $𝐔_{1}$ , $𝐔_{2}$ may be singular. Applications to two examples of the analysis of variance are given.