Higher Dimensional Nonlinear Regression-A Statistical Use of the Riemannian Curvature Tensor

Abstract

Results presented in previous authors papers are extended from the case of a low dimension of the parameter to the case of an arbitrary dimension. In particular, for arbitrary nonlinear regression models with normal errors, we present in an explicit form the “almost exact” density of the maximum likelihood estimator. It is a better approximation than the one obtained by the saddle-point method. In all obtained results the Riemannian curvature tensor is of great importance.