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A study of variable bandwidth selection for local polynomial regression

Jianqing Fan Irne Gijbels Tien-Chung Hu Li-Shan Huang

Statistics Theory and Methods mathscidoc:1912.43294

Statistica Sinica, 113-127, 1996.1
A decisive question in nonparametric smoothing techniques is the choice of the bandwidth or smoothing parameter. The present paper addresses this question when using local polynomial approximations for estimating the regression function and its derivatives. A fully-automatic bandwidth selection procedure has been proposed by Fan and Gijbels (1995a), and the empirical performance of it was tested in detail via a variety of examples. Those experiences supported the methodology towards a great extend. In this paper we establish asymptotic results for the proposed variable bandwidth selector. We provide the rate of convergence of the bandwidth estimate, and obtain the asymptotic distribution of its error relative to the theoretical optimal variable bandwidth. These asymptotic properties give extra support to the proposed bandwidth selection procedure. It is also demonstrated how the proposed selection
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@inproceedings{jianqing1996a,
  title={A study of variable bandwidth selection for local polynomial regression},
  author={Jianqing Fan, Irne Gijbels, Tien-Chung Hu, and Li-Shan Huang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113534001231854},
  booktitle={Statistica Sinica},
  pages={113-127},
  year={1996},
}
Jianqing Fan, Irne Gijbels, Tien-Chung Hu, and Li-Shan Huang. A study of variable bandwidth selection for local polynomial regression. 1996. In Statistica Sinica. pp.113-127. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113534001231854.
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