Classical regression model under zero-excess assumptions

We consider the classical regression model defined by a random vector Xn×1, scalar matrices yn×m, vn×n, a scalar column bm×1 and a scalar s2 satisfying EX = yb, Cov X = s2v and the usual regularity conditions. Using only assumptions, we prove that the classical estimator ŝ2 for s2 in that model is the unique unbiased one with minimum variance in a large class of estimators.