Bayes unbiased estimation in a model with three variance components.(English)Zbl 0689.62026

Summary: Necessary and sufficient conditions for an existence and an explicit expression for the Bayes invariant quadratic unbiased estimate of a linear function of variance components are presented for the mixed linear model $t=X\beta +\epsilon,\quad E(t)=X\beta,\quad Var(t)=\theta_ 1U_ 1+\theta_ 2U_ 2+\theta_ 3U_ 3,$ with three unknown variance components in the normal case. An application to some examples from the analysis of variance is given.

MSC:

 62F15 Bayesian inference 62H12 Estimation in multivariate analysis 62J10 Analysis of variance and covariance (ANOVA) 62J99 Linear inference, regression
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References:

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