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.