Using non-stochastic terms to advantage in kernel-based estimation of integrated squared density derivatives

M. C. Jones, S. J. Sheather

Research output: Contribution to journalArticlepeer-review

115 Scopus citations

Abstract

Improved kernel-based estimates of integrated squared density derivatives are obtained by reinstating non-stochastic terms that have previously been omitted, and using the bandwidth to (approximately) cancel these positive quantities with the leading smoothing bias terms which are negative. Such estimators have exhibited great practical merit in the context of data-based selection of the bandwidth in kernel density estimation, a motivating application of this work discussed elsewhere.

Original languageEnglish
Pages (from-to)511-514
Number of pages4
JournalStatistics and Probability Letters
Volume11
Issue number6
DOIs
StatePublished - Jun 1991

Bibliographical note

Funding Information:
further assistance, to Matt Wand for his useful comment and to the referee for forcing certain clarifications. Both the Mathematical Sciences Research Centre of the Australian National University, Canberra, Australia, and the IBM Research Division, Yorktown Heights, New York, USA, supported M.C. Jones during the course of this work.

Keywords

  • Bandwidth selection
  • bias reduction
  • functional estimation
  • kernel density estimation
  • rates of convergence
  • smoothing

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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