Estimation of mean square error of empirical best linear unbiased predictors under a random error variance linear model

A linear model with random effects, [mu]i, and random error variances, [sigma]i, is considered. The linear Bayes estimator or the best linear unbiased predictor (BLUP) of [mu]i is first obtained, and then the unknown parameters in the model are estimated to arrive at the empirical linear Bayes estimator or the empirical BLUP (EBLUP) of [mu]i. A second-order approximation to mean square error (MSE) of the EBLUP and an approximately unbiased estimator of MSE are derived. Results of a simulation study confirm the accuracy of these approximations.