MSE superiority of Bayes and empirical Bayes estimators in two generalized seemingly unrelated regressions

This paper deals with the estimation problem in a system of two seemingly unrelated regression equations where the regression parameter is distributed according to the normal prior distribution N(β0,σβ2Σβ). Resorting to the covariance adjustment technique, we obtain the best Bayes estimator of the regression parameter and prove its superiority over the best linear unbiased estimator (BLUE) in terms of the mean square error (MSE) criterion. Also, under the MSE criterion, we show that the empirical Bayes estimator of the regression parameter is better than the Zellner type estimator when the covariance matrix of error variables is unknown.