Low-order nonparametric enhancements of parametric curve estimators

Research Report SRR97-013

Low-order nonparametric enhancements of parametric curve estimators

Ming-Yen Cheng, Peter Hall, Berwin Turlach

Abstract: 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 first fit 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 differences between low-order parametric and nonparametric fits, since we effectively remove all the low-order parametric information and replace it by nonparametric information. Thus, we employ parametric 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.

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