The Improved Estimates of Regression Coefficientsin Seemingly Unrelated Regression Model withTwo Equations

For regression coefficients in seemingly unrelated regression model with two equations, this paper obtains a two-stage covariance improved estimator sequence by using the covariance improved idea for reference. The condition under which this improved estimator is equivalent to the classic two-stage estimator and the optimal property on the term of mean square error are also obtained. And then, by improving the two-stage estimator in the literature, this paper derives a new improved estimator which shows small sample property relative to least square estimator in more wide parameters space. Through a ultimate way, this paper provides a new estimator which have better small sample property. Finally, this paper discusses the optimal property of two-stage estimator under the Pitman criterion.