A SEMIPARAMETRIC MAXIMUM-LIKELIHOOD ESTIMATOR

This paper presents a procedure for analyzing a model in which the par ameter vector has two parts: a finite-dimensional component theta and a nonparametric component lambda. The procedure does not require param etric modeling of lambda but assumes that the true density of the data satisfies an index restriction. The idea is to construct a parametric model passing through the true model and to estimate theta by setting the score for the parametric model to zero. The score is estimated no nparametrically and the estimator is shown to be root N consistent and asymptotically normal. The estimator is then shown to attain the semi parametric efficiency bound characterized in Begun et al. (1983) for m ultivariate nonlinear regression, simultaneous equations, partially sp ecified regression, index regression, censored regression, switching r egression, and disequilibrium models in which the error densities are unknown.