Relative stability of global errors of nonparametric function estimators

L. Györfi, Dominik Schäfer, Harro Walk

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

This paper presents relative stability properties of various nonparametric density estimators (histogram, kernel estimates) and of regression estimators (partitioning, kernel, and nearest neighbor estimates). In density estimation, let E n denote the L 1 error of an estimate calculated from n data, whereas in regression estimation, the L 2 error of the estimate is used. Sufficient conditions for E n/E{E n} → 1 in probability are provided. If this limit holds, the asymptotic behavior of the random error E n can be characterized by its expectation E{E n}, and one may apply, for example, the established rate-of-convergence results for E{E n}.

Original languageEnglish
Pages (from-to)2230-2242
Number of pages13
JournalIEEE Transactions on Information Theory
Volume48
Issue number8
DOIs
Publication statusPublished - Aug 2002

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Random errors
regression

Keywords

  • Nonparametric density estimation
  • Nonparametric regression estimation
  • Relative stability

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Information Systems

Cite this

Relative stability of global errors of nonparametric function estimators. / Györfi, L.; Schäfer, Dominik; Walk, Harro.

In: IEEE Transactions on Information Theory, Vol. 48, No. 8, 08.2002, p. 2230-2242.

Research output: Contribution to journalArticle

Györfi, L. ; Schäfer, Dominik ; Walk, Harro. / Relative stability of global errors of nonparametric function estimators. In: IEEE Transactions on Information Theory. 2002 ; Vol. 48, No. 8. pp. 2230-2242.
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