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Rates of convergence for the pre-asymptotic substitution bandwidth selector

Jianqing Fan Li-Shan Huang

Statistics Theory and Methods mathscidoc:1912.43390

Statistics & probability letters, 43, (3), 309-316, 1999.7
An effective bandwidth selection method for local linear regression is proposed in Fan and Gijbels [1995, J. Roy. Statist. Soc. Ser. B, 57, 371394]. The method is based on the idea of the pre-asymptotic substitution and has been tested extensively. This paper investigates the rate of convergence of this method. In particular, we show that the relative rate of convergence is of order <i>n</i><sup>2/7</sup> if the locally cubic fitting is used in the pilot stage, and the rate of convergence is <i>n</i><sup>2/5</sup> when the local polynomial of degree 5 is used in the pilot fitting. The study also reveals a marked difference between the bandwidth selection for nonparametric regression and that for density estimation: The plug-in approach for the latter case can admit the root-<i>n</i> rate of convergence while for the former case the best rate is of order <i>n</i><sup>2/5</sup>.
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@inproceedings{jianqing1999rates,
  title={Rates of convergence for the pre-asymptotic substitution bandwidth selector},
  author={Jianqing Fan, and Li-Shan Huang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114120345850950},
  booktitle={Statistics &amp; probability letters},
  volume={43},
  number={3},
  pages={309-316},
  year={1999},
}
Jianqing Fan, and Li-Shan Huang. Rates of convergence for the pre-asymptotic substitution bandwidth selector. 1999. Vol. 43. In Statistics &amp; probability letters. pp.309-316. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114120345850950.
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