Prediction of random effects in finite mixture models with Gaussian components

Prediction of random effects in finite mixture models with Gaussian distributions is discussed from a non-Bayesian perspective, assuming that location and dispersion parameters are known. The focus is on calculating the best predictor, that is, the statistic with minimum expected squared prediction error, for several models. Coverage includes mixture sampling models, as well as mixtures for the distribution of the random effects. Longitudinal and cross-sectional specifications with correlated random effects, such as those arising in animal breeding and genetics, are examined. The best linear predictor and the best linear unbiased predictor are derived for these models as well.