The robustness of BLUP and EBLUP

The expectations of BLP and BLUP used as estimator for fixed effects and as predictor for random effects were investigated concerning the property 'un biasedness'. Different aspects of robustness research on prediction procedu res are discussed. The robustness of BLUP and EBLUP was investigated with r espect to the distribution of the random components of the model, the degre e of balancedness of the experimental design, influence of the variance com ponents ratio and different variance component estimators used in EBLUP(2) on the bases of a computer simulation in the random one-way model. Criteria used for the evaluation were the mean squared error (MSE) and the selectio n gain. Besides, an idea of the overestimation of the accuracy of EBLUP by the naive MSE approximation based on the MSE formulas of BLUP with variance component estimations instead of unknown parameters is given.