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

AbstractA linear model with random effects, μi, and random error variances, σi, is considered. The linear Bayes estimator or the best linear unbiased predictor (BLUP) of μi 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 μi. 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