The focus of this paper is to discuss the statistical properties of several two stage estimators of the regression coefficients (β) in seemingly unrelated regression system with unequal numbers of observations(SURS(UNO)) when the covariance matrix unknown.

Firstly, we give the expression of root root estimator and proved under some condition root root estimator is more efficient than the Covariance Adjusted Approach, and the properties are also discussed for the two-stage estimator.

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.

Also discuss the qualities about the estimate and its two-stage estimate.

Firstly,a simple computing method is given for the two-stage estimate of regression coefficient matrix in the Growth Curve Model with Random Effects.

Chapter 3 is devoted to discuss the two-stage estimate of KθL,which mainly included two s.

After having reviewed the basic collocation theory, the principle of the collocation by two minimization steps is introduced.

The 2SLS estimator is an estimator has good properties with large sample and finite sample when the the instruments are chosen legitimate ,but if the instruments are not chosen legitimate ,especially weekly correlated with the endogenous explanatory variables ,the 2SLS estimator will be biasd badly.