On the L1-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 L1-error of the classical histogram density estimator is calculated in any dimension. The asymptotic distribution of the standardized L1-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
DOIs
Publication statusPublished - Jan 1 1998

Keywords

  • Asymptotic normality
  • Density estimation
  • Histogram estimators

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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