A Generalization of the Gauss-Markov Theorem
Truman O. Lewis, Patrick L. Odell · Journal of the American Statistical Association · 1966
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.