Improved Estimator For The Common Parameter In Two Seemingly Unrelated Regressions

Linear Regression model is a kind of important statistic model with wide application, and Seemingly Unrelated Regression model is a kind of special linear regression model. In this article, we mainly discuss the parameter estimation of the seemingly unrelated regression model made up by two regression equations with the common parameter.We firstly introduce how to construct the common least square estimate, the general least square estimate, the covariance-adjusted estimator and the two-stage estimator. According to covariance-adjusted method, we obtain a series of covariance-adjusted estimators for the common parameter, and come to two unique simpler version for the two covariance-adjusted estimator from the series of estimators under the condition of Zellner's assumption. Next, combining with the theory of the two-stage estimator, we propose the two-stage covariance-adjusted estimator of the model by using sample covariance to replace. Thirdly, based on the weighted method, we find a kind of weight coefficient from the BLUE's shape of the parameter, and get the weighted two-stage covariance-adjusted estimator for the common parameter of the regression model. Meanwhile we give the proof that the weighted two-stage covariance-adjusted estimator is superior to the common least square estimate in terms of mean square error(MSE) criterion.Finally, we verify the weighted two-stage covariance-adjusted estimator by numerical simulation and prove the improved estimator is better than the common least square estimate in terms of MSE criterion.