The blue and minque in Gauss-Markoff model with linear transformation of the observable variables*

For a singular linear model A=(y,Xβ,σV) and its transformed model AF=(Fy,FXβσ2FVF1), where V is nonnegative definite and X can be rank-deficient, the expressions for the differences of the estimates for the vector of FXβ and the variance factor σ2 are given. Moreover, the necessary and sufficient conditions for the equalities of the estimates for the vector of FXβ and the variance factor σ2 are also established. In the meantime, works in Baksalary and Kala (1981) are strengthened and consequences in Puntanen and Nurhonen (1992), and Puntanen (1996) are extended.