Low-order Nonparametric Enhancements of Parametric Curve Estimators

We suggest a method for using nonparametric information to modify a parametric model at a low-order level, retaining information in the model only to enhance the nonparametric approach at relatively high orders. Our technique represents an alternative to methods that rst t a parametric model and then adjust it. In particular, relative to a \nonparametric estimator with a parametric start," our estimator is not biased by the diierences between low-order paramet-ric and nonparametric ts, since we eeectively remove all the low-order parametric information and replace it by nonparametric information. Thus, we employ para-metric information only when the nonparametric information is unreliable, and do not use it elsewhere. The method has application to both nonparametric density estimation and nonparametric regression.