Linear Transformations Preserving Best Linear Unbiased Estimators in a General Gauss-Markoff Model

Abstract

Under a general Gauss-Markoff model $\{\mathbf{y}, \mathbf{X,\beta, V}\}$, a necessary and sufficient condition is established for a linear transformation, $\mathbf{F}$, of the observable random vector $\mathbf{y}$ to have the property that there exists a linear function of $\mathscr{Fy}$ which is a BLUE of $\mathbf{X\beta}$. A method for deriving a required BLUE from the transformed model $\{\mathbf{Fy, FX\beta, FVF}'\}$ is also indicated.