On the L 1-error in histogram density estimation

The multidimensional case

J. Beirlant, L. Györfi

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Under some smoothness and tail conditions on the density the rate of convergence of the expected L 1-error of the classical histogram density estimator is calculated in any dimension. The asymptotic distribution of the standardized L 1-error is derived under minimal conditions. In particular, a sharp uniform rate for the variance of the error is established and explicit representations of the asymptotic variance of the error are given.

Original languageEnglish
Pages (from-to)197-216
Number of pages20
JournalJournal of Nonparametric Statistics
Volume9
Issue number2
Publication statusPublished - 1998

Fingerprint

Density Estimation
Histogram
Density Estimator
Asymptotic Variance
Asymptotic distribution
Tail
Smoothness
Rate of Convergence
Density estimation

Keywords

  • Asymptotic normality
  • Density estimation
  • Histogram estimators
  • L -error

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

On the L 1-error in histogram density estimation : The multidimensional case. / Beirlant, J.; Györfi, L.

In: Journal of Nonparametric Statistics, Vol. 9, No. 2, 1998, p. 197-216.

Research output: Contribution to journalArticle

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