A crossvalidation method for estimating conditional densities

Jianqing Fan, Tsz Ho Yim

Research output: Contribution to journalArticle

76 Scopus citations

Abstract

We extend the idea of crossvalidation to choose the smoothing parameters of the 'double-kernel' local linear regression for estimating a conditional density. Our selection rule optimises the estimated conditional density function by minimising the integrated squared error. We also discuss three other bandwidth selection rules, an ad hoc method used by Fan et al. (1996), a bootstrap method of Hall et al. (1999) for bandwidth selection in the estimation of conditional distribution functions, modified by Bashtannyk & Hyndman (2001) to cover conditional density functions, and finally a simple approach proposed by Hyndman & Yao (2002). The performance of the new approach is compared with these three methods by simulation studies, and our method performs outstandingly well. The method is illustrated by an application to estimating the transition density and the Value-at-Risk of treasury-bill data.

Original languageEnglish (US)
Pages (from-to)819-834
Number of pages16
JournalBiometrika
Volume91
Issue number4
DOIs
StatePublished - Dec 1 2004
Externally publishedYes

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

  • Bandwidth selection
  • Bootstrap
  • Conditional density function
  • Crossvalidation
  • Diffusion process
  • Financial application
  • Transition density

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