High-derivative parametric enhancements of nonparametric curve estimators
Resource
Biometrika 86(2),417-428
Journal
Biometrika 86
Pages
417-428
Date Issued
1999
Date
1999
Author(s)
DOI
2006092712112422698
Abstract
We suggest a method for using parametric information to modify a nonparametric estimator at the level of relatively high-order derivatives. The 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 parametric and nonparametric fits to low-order derivatives, since we effectively remove all the parametric information about low-order derivatives and replace it by nonparametric information. Thus, we employ parametric information only when the 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.
Subjects
Bias reduction
Curve estimation
Density estimation
Kernel regression
Local polynomial regression
Locally parametric methods
Log-polynomial model
Nonparametric regression
Type
journal article
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