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 (1998 Glad , I. ( 1998 ). Parametrically guided non-parametric regression . Scandinavian Journal of Statistics 25 : 649 – 668 .[Crossref], [Web of Science ®] , [Google Scholar]). We show that under fairly mild conditions the estimators in the proposed class are asymptotically normal and explore their finite sample (simulation) behavior.