Evaluation of the Best Linear Unbiased Prediction in Mixed Linear Models with Estimated Variance Components by Means of the MSE of Prediction and the Genetic Selection Differential

Abstract

Prediction in mixed linear models by Henderson's (1972) BLUP (Best Linear Unbiased Prediction) requires knowledge of the underlying variance/covariance components to have the property ‘best’. In breeding value prediction these parameters are not known, generally. They have to be replaced by estimations and BLUP becomes estimated BLUP (EBLUP). The aim of this investigation was the evaluation of EBLUP with help of a designed simulation experiment. Criteria used for the evaluation were the mean squared error (MSE) and the (genetic) selection differential (GSD). 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.