Maximum Likelihood and Iterated Aitken Estimation of Nonlinear Systems of Equations

Abstract

For nonlinear equation systems, the properties of the MLE commonly have been deduced from related but inapplicable results in the statistical and econometric literature. Under specific regularity conditions, we build on the nonlinear GLS results of Malinvaud to derive the large-sample properties of the MLE and the limiting distribution of the asymptotic likelihood ratio statistic. We discuss iterative convergence conditions under which the iterated Aitken estimator locates a consistent local maximum of the likelihood function, and we derive results permitting convenient estimation of the asymptotic covariance matrix of any subset of parameter estimators.