A BLUE decomposition in the general linear regression model Original Research Article

In this note we consider the general linear regression model (y,Xβ,VR2β2 = r) where the block partitioned regressor matrix X = (X1 X2) may be deficient in column rank, the dispersion matrix V is possibly singular, βt = (βt1 βt2)—being partitioned according to X—is the vector of unknown regression coefficients, and β2 is possibly subject to consistent linear constraints R2β2 = r. Of much interest to us is the traditional BLUE (best linear unbiased estimator) of Xβ. We show how this traditional BLUE can obtained from the traditional BLUE of X1β1 in the related model (y, X1β1, V). Some properties of the dispersion matrix of the traditional BLUE of Xβ are also given.