The Hilbert Kernel Regression Estimate

Luc Devroye, L. Györfi, Adam Krzyzak

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Let (X, Y) be an Rd×R-valued regression pair, whereXhas a density andYis bounded. Ifni.i.d. samples are drawn from this distribution, the Nadaraya-Watson kernel regression estimate in Rdwith Hilbert kernelK(x)=1/xdis shown to converge weakly for all such regression pairs. We also show that strong convergence cannot be obtained. This is particularly interesting as this regression estimate does not have a smoothing parameter.

Original languageEnglish
Pages (from-to)209-227
Number of pages19
JournalJournal of Multivariate Analysis
Volume65
Issue number2
DOIs
Publication statusPublished - May 1998

Fingerprint

Regression Estimate
Kernel Regression
Kernel Estimate
Hilbert
Regression
Smoothing Parameter
Strong Convergence
Converge
Kernel regression

Keywords

  • Bandwidth selection
  • Convergence
  • Kernel estimate
  • Nadaraya-Watson estimate
  • Nonparametric estimation
  • Regression function estimation

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Numerical Analysis
  • Statistics and Probability

Cite this

The Hilbert Kernel Regression Estimate. / Devroye, Luc; Györfi, L.; Krzyzak, Adam.

In: Journal of Multivariate Analysis, Vol. 65, No. 2, 05.1998, p. 209-227.

Research output: Contribution to journalArticle

Devroye, Luc ; Györfi, L. ; Krzyzak, Adam. / The Hilbert Kernel Regression Estimate. In: Journal of Multivariate Analysis. 1998 ; Vol. 65, No. 2. pp. 209-227.
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