Kernel density estimation with spherical data

Peter Hall, G. S. Watson, Javier Cabrera

Research output: Contribution to journalArticlepeer-review

128 Scopus citations

Abstract

We study two natural classes of kernel density estimators for use with spherical data. Members of both classes have already been used in practice. The classes have an element in common, but for the most part they are disjoint. However, all members of the first class are asymptotically equivalent to one another, and to a single element of the second class. In this sense the second class 'contains' the first. It includes some estimators which out-perform all those in the first class, if loss is measured in either squared-error or Kullback-Leibler senses. Explicit formulae are given for bias, variance and loss, and large-sample properties of these quantities are described. Numerical illustrations are presented.

Original languageEnglish (US)
Pages (from-to)751-762
Number of pages12
JournalBiometrika
Volume74
Issue number4
DOIs
StatePublished - Dec 1 1987

All Science Journal Classification (ASJC) codes

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

Keywords

  • Bias
  • Cross-validation
  • Kernel density estimation
  • Loss
  • Spherical data
  • Variance

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