A maximal extension of the Gauss-Markov Theorem and its nonlinear version

Abstract

In this paper, first we make a maximal extension of the well-known Gauss-Markov Theorem (GMT) in its linear framework. In particular, the maximal class of distributions of error term for which the GMT holds is derived. Second, we establish a nonlinear version of the maximal GMT and describe some interesting families of distributions of error term for which the nonlinear GMT holds. © 2002 Elsevier Science (USA).