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On Superiority of Estimation Regarding Pitman Closeness Criterion in General Mixed Linear Models

The general mixed linear model can be written as y = X γ + Zu + e . In the short note, we mainly aim to apply Pitman closeness criterion to a mixed linear model. The problem of estimating the objective function as a linear combination of fixed effects and random effects, μ = L ′γ + M ′ u , is considered. We denote by (resp. μ*) the best linear unbiased estimate when γ is known (resp. unknown) of μ and by the ordinary least squares solution of γ. Two problems are handled in sequence. Firstly, we prove that and μ* are superior over with respect to Pitman closeness criterion by using the median unbiasedness techniques. After that, the main results are applied to Bayes arguments.