Estimation of some partially specified nonlinear models

This paper presents a procedure for analyzing a partially specified nonlinear regression model in which the nuisance parameter is an unrestricted function of a subset of regressors. The procedure does not require parametric modeling of the nuisance parameter but assumes that the model can be transformed into a partially specified linear equation by inverting some nonlinear functions. The model parameters are estimated by applying Robinson's (1988a) procedure and the estimator is shown to be root N-consistent and asymptotically normal. One attraction of the estimator is that it is computationally simple, requiring no more than least squares regressions. A simulation study indicates that the estimator has practical values.