Covariance Adjusted Approach and Parameter Estimation in Seemingly Unrelated Regression

For a seemingly unrelated regression with two linear regressionb models, a sequence of estimators is proposed by using the covariance adjusted approach. It is proved that the sequence converges everywhere to the best linear unbised estimator（BLUE） and their covariance matrices converge monotonically to that of the BLUE if the covariance matrix of the errors is known. The sequence has also some optimalities under Pitman criterion of closeness. When the covariance matrix of the errors is undnown, the unbiasedness, the consistency and the saymptotic normaluity of the two-stage estimators of the sequence are proved. The results obtained in this paper show also the power of the covariance adjusted approach.