Prediction in a class of mixed models with two variance components

A best unbiased predictor (BUP) of an arbitrary linear combination of fixed and random effects in mixed linear models is available when the true values of the variance ratios are known. When the true values are unknown, a two-stage predictor, obtained from the BUP by replacing the true values by estimated values, can be used. In this article, exact mean squared errors of two-stage predictors are obtained for a class of mixed models with two variance components that includes the balanced one-way random model and other analysis-of-variance models with proportional frequencies and one balanced random factor.