On the use of the directional derivative in obtaining multivariate extreme values

Abstract

Current use of the directional derivative appears, with notable exceptions such as Whittle (1971, 1973) and Vainberg (1973), to be limited largely to textbooks on advanced calculus, and to spaces of at most three dimensions. The present paper develops a calculus of the directional derivative for arbitrary finite dimensional vector spaces. Applications are made to classical maximum likelihood estimation in the case of the multivariate normal density and to other multivariate problems involving stationary points.