High-derivative parametric enhancements of nonparametric curve estimators

被引:7
|
作者
Cheng, MY [1 ]
Hall, P
Turlach, BA
机构
[1] Natl Taiwan Univ, Dept Math, Taipei 106, Taiwan
[2] Australian Natl Univ, Ctr Math & Its Applicat, Canberra, ACT 0200, Australia
[3] Univ Adelaide, Dept Stat, Adelaide, SA 5005, Australia
关键词
bias reduction; curve estimation; density estimation; kernel regression; local polynomial regression; locally parametric methods; log-polynomial model; nonparametric regression;
D O I
10.1093/biomet/86.2.417
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
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 is unreliable, and do not use it elsewhere. The method has application to both nonparametric density estimation and nonparametric regression.
引用
收藏
页码:417 / 428
页数:12
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