Covariance-Improved Estimator of Generalized Seemingly Unrelated Regression Equations System

For the system of Seemingly Unrelated Regression Equations given by \left\\beginarrayly_1=X_1 \beta+U_1 \\ y_2=X_2 \gamma+U_2\endarray\right.（in this two linear regression models, y₁ is a matrix of m×1, y₂ is a matrix of n×1, m ≠ n）, we obtained am iteration sequence of estimator by using the covariance-improved approach. It is proved that the sequence converges everywhere to the best linear unbiased estimator （BLUE） and their covariance matrixes converge monotonically to that of the BLUE if the covariance matrixof the errors is known.
When the covariance matrix of the errors is unknown, we consider the optimality of the two-stage covariance improved estimator. Under normal distribution assumption on the random error, the unbiasedness, the asymptotic normality and the strong consistency of the two-stage estimator are proved. Furthmore, a weak consistency condition is obtained when the iteration step is infinite.
In this paper we extended and improved the covariance-improved estimator introduced by Wang Songgui, the results show clearly the power of the covariance-improved approach.