An Improved Estimator of the Density Function at the Boundary

S. Zhang, R. J. Karunamuni, M. C. Jones

Research output: Contribution to journalArticlepeer-review

68 Scopus citations


We propose a new method of boundary correction for kernel density estimation. The technique is a kind of generalized reflection method involving reflecting a transformation of the data. The transformation depends on a pilot estimate of the logarithmic derivative of the density at the boundary. In simulations, the new method is seen to clearly outperform an earlier generalized reflection idea. It also has overall advantages over boundary kernel methods and a nonnegative adaptation thereof, although the latter are competitive in some situations. We also present the theory underlying the new methodology.

Original languageEnglish (US)
Pages (from-to)1231-1240
Number of pages10
JournalJournal of the American Statistical Association
Issue number448
StatePublished - Dec 1 1999
Externally publishedYes


  • Density estimation
  • Mean squared error
  • Pseudodata
  • Reflection
  • Transformation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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