On optimal data-based bandwidth selection in Kernel density estimation

Peter Hall, Simon J. Sheather, M. C. Jones, J. S. Marron

Research output: Contribution to journalArticlepeer-review

186 Scopus citations


A bandwidth selection method is proposed for Kernel density estimation. This is based on the straightforward idea of plugging estimates into the usual asymptotic representation for the optimal bandwidth, but with two important modifications. The result is a bandwidth selector with the, by nonparametric standards, extremely fast asymptotic rate of convergence of n-2-Jan where n ↑ ∞ denotes sample size. Comparison is given to other bandwidth selection methods, and small sample impact is investigated.

Original languageEnglish
Pages (from-to)263-269
Number of pages7
Issue number2
StatePublished - Jun 1991

Bibliographical note

Funding Information:
M. C. Jones was supported by a Mathematical Sciences Research Centre Visiting Fellowship at the Australian National University. J. S. Marron was supported by the National Science Foundation.


  • Adaptive procedure
  • Convergence rate
  • Functional estimation
  • Mean integrated squared error
  • Smoothing parameter
  • Taylor expansion
  • Window width

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Agricultural and Biological Sciences (miscellaneous)
  • General Agricultural and Biological Sciences
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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