Some further remarks on the singular linear model Original Research Article

Inspired by a recent article of Searle (1994), we consider some specific features of estimation of Xβ in the general linear model {y, Xβ, V}, where the model matrix X need not have full column rank and the dispersion matrix V can be singular. Particular attention is paid to the problems related to the invariance of some matrix expressions with respect to the choice of generalized inverses. These invariance properties yield interesting matrix algebra while characterizing the best linear unbiased estimator of Xβ.