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.


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