A Generalization of the Gauss-Markov Theorem

Abstract

Abstract This paper contains a generalization of the Gauss Markov Theorem based on the properties of the generalized inverse of a matrix as defined by Penrose. A minimum variance vector estimate of a parameter vector x is given for the linear model of less than full rank. Since linear unbiased estimates may not always exist for this case the unbiased constraint is replaced by the more general constraint that the norm is minimized.