Estimating Nonlinear Models by Maximum Likelihood for the Exponential Family

Abstract

Many but not all attractive properties of generalized linear models associated with the exponential family of distributions are destroyed by nonlinearity. A consequence is that ensuring the stability of a computational process for maximizing the likelihood becomes relatively more important. Here it is shown that trust region methods for solving nonlinear least squares problems are readily adapted to maximize likelihoods based on the exponential family, and that the nice theoretical results available for the nonlinear least squares problem also generalize.