A study of variable bandwidth selection for local polynomial regression

Jianqing Fan, Irène Gijbels, Tien Chung Hu, Li Shan Huang

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82 Scopus citations


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 method can be applied in the density estimation setup. Some examples illustrate this application.

Original languageEnglish (US)
Pages (from-to)113-127
Number of pages15
JournalStatistica Sinica
Issue number1
StatePublished - 1996
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Assessment of bias and variance
  • Asymptotic normality
  • Binning
  • Density estimation
  • Local polynomial fitting
  • Variable bandwidth selector


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