Local Nonlinear Least Squares Estimation: Using Parametric Information Nonparametrically

We introduce a new kernel smoother for nonparametric regression that uses prior information on regression shape in the form of a parametric model. In effect, we nonparametrically encompass the parametric model. We derive pointwise and uniform consistency and the asymptotic distribution of our procedure. It has superior performance to the usual kernel estimators at or near the parametric model. It is particularly well motivated for binary data using the probit or logit parametric model as a base. We include an application to the Horowitz (1993) transport choice dataset.