Bayes and empirical Bayes iteration estimators in two seemingly unrelated regression equations

For a system of two seemingly unrelated regression equations given by {y1 = X-1 beta + epsilon(1), y2 = X-2 gamma + epsilon(2), (y(1) is an m x 1 vector and y(2) is an n x 1 vector, m not equal n), employing the covariance adjusted technique, we propose the parametric Bayes and empirical Bayes iteration estimator sequences for regression coefficients. We prove that both the covariance matrices converge monotonically and the Bayes iteration estimator squence is consistent as well. Based on the mean square error (MSE) criterion, we elaborate the superiority of empirical Bayes iteration estimator over the Bayes estimator of single equation when the covariance matrix of errors is unknown. The results obtained in this paper further show the power of the covariance adjusted approach.