Maximization by parts in extremum estimation

Abstract

In this paper, we present various iterative algorithms for extremum estimation in cases where direct computation of the extremum estimator or via the Newton-Ralphson algorithm is di¢ cult, if not impossible. While the Newton-Ralphson algorithm makes use of the full Hessian matrix which may be di¢ cult to evaluate, our algorithms use parts of the Hessian matrix only, the parts that are easier to compute. We establish convergence and asymptotic properties of our algorithms under regularity conditions including the information dominance conditions. We apply our algorithms to the estimation of Merton’s structural credit risk model.