Boundary aware estimators of integrated density derivative products

Ming Yen Cheng*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

33 Citations (Scopus)


Integrated squared density derivatives are important to the plug-in type of bandwidth selector for kernel density estimation. Conventional estimators of these quantities are inefficient when there is a non-smooth boundary in the support of the density. We introduce estimators that utilize density derivative estimators obtained from local polynomial fitting. They retain the rates of convergence in mean-squared error that are familiar from non-boundary cases, and the constant coefficients have similar forms. The estimators and the formula for their asymptotically optimal bandwidths, which depend on integrated products of density derivatives, are applied to automatic bandwidth selection for local linear density estimation. Simulation studies show that the constructed bandwidth rule and the Sheather–Jones bandwidth are competitive in non-boundary cases, but the former overcomes boundary problems whereas the latter does not.

Original languageEnglish
Pages (from-to)191-203
Number of pages13
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Issue number1
Publication statusPublished - Jan 1997

User-Defined Keywords

  • Bandwidth Selection
  • Boundary Effects
  • Data Binning
  • Local Polynomial Fitting
  • Plug-In Bandwidth Selector


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