CONSISTENT MAXIMUM LIKELIHOOD ESTIMATION OF THE NONLINEAR REGRESSION MODEL WITH NORMAL ERRORS

Abstract

Standard consistency proofs of the maximum likelihood estimator rely on the assumption that the observations are independent and identically distributed. In econometric models, however, this assumption is seldom satisfied. In this paper we prove consistency of the maximum likelihood estimator obtained from observations (not necessarily independent or identically distributed), whose joint distribution is known to be normal. This contains the nonlinear regression model with normal errors as a special case. Our regularity conditions appear to be mild; in particular, no uniform convergence assumption is made. An example (first-order autocorrelation) demonstrates the easy applicability of our conditions.