Strongly consistent density estimation of the regression residual

L. Györfi, Harro Walk

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Consider the regression problem with a response variable Y and with a d-dimensional feature vector X. For the regression function m(x)=E{Y{pipe}X=x}, this paper investigates methods for estimating the density of the residual Y-m(X) from independent and identically distributed data. For heteroscedastic regression, we prove the strong universal (density-free) L 1-consistency of a recursive and a nonrecursive kernel density estimate based on a regression estimate.

Original languageEnglish
Pages (from-to)1923-1929
Number of pages7
JournalStatistics and Probability Letters
Volume82
Issue number11
DOIs
Publication statusPublished - Nov 2012

Fingerprint

Consistent Estimation
Density Estimation
Regression
Heteroscedastic Regression
Kernel Density Estimate
Regression Estimate
Regression Function
Feature Vector
Identically distributed
Density estimation

Keywords

  • Heteroscedastic regression
  • Nonparametric kernel density estimation
  • Nonparametric regression estimation
  • Primary
  • Regression residual
  • Secondary

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Statistics and Probability

Cite this

Strongly consistent density estimation of the regression residual. / Györfi, L.; Walk, Harro.

In: Statistics and Probability Letters, Vol. 82, No. 11, 11.2012, p. 1923-1929.

Research output: Contribution to journalArticle

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