The term ``empirical predictor'' refers to a two-stage predictor of a linear
combination of fixed and random effects. In the first stage, a predictor is
obtained but it involves unknown parameters; thus, in the second stage, the
unknown parameters are replaced by their estimators. In this paper, we consider
mean squared errors (MSE) of empirical predictors under a general setup, where
ML or REML estimators are used for the second stage. We obtain second-order
approximation to the MSE as well as an estimator of the MSE correct to the same
order. The general results are applied to mixed linear models to obtain a
second-order approximation to the MSE of the empirical best linear unbiased
predictor (EBLUP) of a linear mixed effect and an estimator of the MSE of EBLUP
whose bias is correct to second order. The general mixed linear model includes
the mixed ANOVA model and the longitudinal model as special cases
