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Bayes unbiased estimation in a model with two variance components. (English) Zbl 0625.62019
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 linar model \(t=X\beta +\epsilon\), \(E(t)=X\beta\), \(D(t)=\theta_ 1U_ 1+\theta_ 2U_ 2\) with the unknown variance components in the normal case. The matrices \(U_ 1\), \(U_ 2\) may be singular. Applications to two examples of the analysis of variance are given.

62F15 Bayesian inference
62J10 Analysis of variance and covariance (ANOVA)
62J99 Linear inference, regression
62C15 Admissibility in statistical decision theory
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