A class of improved parametrically guided nonparametric regression estimators

In this article we define a class of estimators for a nonparametric regression model with the aim of reducing bias. The estimators in the class are obtained via a simple two-stage procedure. In the first stage, a potentially misspecified parametric model is estimated and in the second stage the parametric estimate is used to guide the derivation of a final semiparametric estimator. Mathematically, the proposed estimators can be thought as the minimization of a suitably defined Cressie.Read discrepancy that can be shown to produce conventional nonparametric estimators, such as the local polynomial estimator, as well as existing two-stage multiplicative estimators, such as that proposed by Glad (Citation1998). We show that under fairly mild conditions the estimators in the proposed class are asymptotically normal and explore their finite sample (simulation) behavior.