Improvement Of Parameter Estimators In Seemingly Unrelated Regression Model

The article discusses the best linear unbiased Bayes estimators of parameters in Seemingly Unrelated Regression Model(m=2). In the firstpart, under the assumption of X1X2=0, we present the best linear unbiased Bayes estimators of SUR, the estimator is better than the ordinary least square estimator(LSE) and the best linear unbiased estimator(BLUE) in term of the loss matrix criterion , furthermore, the estimator is superior to LSE under the posterior Pitman closeness(PPC) criterion. In the second part, when the design matrix is ill-conditioned, we propose two shrunken principal estimators and the related two-stage estimators, we prove the superiority to Covariance Improvement estimator and two-stage Covariance Improvement estimator under the mean square error and the admissibility in the class of linear estimators, finally, we give a method to find the solution of...