A Maximal Extension of the Gauss–Markov Theorem and Its Nonlinear Version

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.