Rates of convergence for the pre-asymptotic substitution bandwidth selector

Jianqing Fan, Li Shan Huang

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


An effective bandwidth selection method for local linear regression is proposed in Fan and Gijbels [1995, J. Roy. Statist. Soc. Ser. B, 57, 371-394]. 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 n-2/7 if the locally cubic fitting is used in the pilot stage, and the rate of convergence is n-2/5 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-n rate of convergence while for the former case the best rate is of order n-2/5.

Original languageEnglish (US)
Pages (from-to)309-316
Number of pages8
JournalStatistics and Probability Letters
Issue number3
StatePublished - Jul 1 1999
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Bandwidth selection
  • Convergence rate
  • Kernel density estimation
  • Local polynomial regression


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