The BLUE in the General Gauss-Markoff Model with Linear Transformations of the Observable Variables

Under an arbitrary rank general Gauss-Markoff model Y =Xβ+ε,ε~（0, ∑）, where∑ is a nennegative definite matrix, the effect of transforming the observable variable vector \tildeY = FY is investigated and the general results of difference of the best linear unbiased estimators （BLUE） of C’β due to the transformations are obtained. The result of linear transformations preserving BLUE in the general Gauss-Markoff model is get as a corollary in this paper. It is shown that the effect of the transformations may be analyzed through an associated regression problem which is amenable to solution by two-step least squares.