A General Procedure for Obtaining Maximum Likelihood Estimates in Generalized Regression Models

CONSIDER THE PROBLEM of maximizing a function f with respect to two variables (or two sets of variables) a1 and a2 within some space S. Suppose it is difficult to maximizefas a function of a1 and a2, but relatively easy to maximizef as a function of a1 given a2 and as a function of a2 given a1. Such a case is frequently encountered in connection with maximum likelihood or quasi-maximum likelihood estimation of certain regression models.2 In this case it is advantageous to adopt a zig-zag iterative procedure which is described below. This procedure was used by Sargan [3] for the purpose of estimating regressions with autoregressive disturbances, but it is amenable to a much more general class of estimation problems. In particular, it can be advantageously used in all cases involving the application of iterative Aitken methods. The plan of the paper is as follows. In Section 2, we present the fundamental lemma and give a proof of convergence in the general case. In Section 3, we demonstrate the applicability of the lemma to the generalized regression model. The last section contains some specific applications that are of interest to econometricians.