Mean square error matrix comparisons of optimal and classical predictors and estimators in linear regression

Abstract Predicting future values of the dependent variable in the general linear regression model essentially is based on two alternative methods: The classical one which estimates the expected value of the regressand to be predicted, and the optimal one which minimizes some quadratic risk over a chosen class of predictors under given specifications of the model. After deriving some characterizations we introduce the mean square error of prediction (MSEP) as the usual measure to compare predictors. It is shown that there are close relations between MSE-superiority of linear estimators and MSEP-superiority of predictors.