Rate of convergence of the density estimation of regression residual

L. Györfi, Harro Walk

Research output: Contribution to journalArticle

1 Citation (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|X = x}, this paper investigates methods for estimating the density of the residual Y - m(X) from independent and identically distributed data. If the density is twice differentiable and has compact support then we bound the rate of convergence of the kernel density estimate. It turns out that for d ≤ 3 and for partitioning regression estimates, the regression estimation error has no influence on the rate of convergence of the density estimate.

Original languageEnglish
Pages (from-to)55-74
Number of pages20
JournalStatistics and Risk Modeling
Volume30
Issue number1
DOIs
Publication statusPublished - Jan 1 2013

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Density Estimation
Error analysis
Rate of Convergence
Regression
Kernel Density Estimate
Regression Estimate
Regression Estimation
Density Estimates
Compact Support
Regression Function
Estimation Error
Feature Vector
Identically distributed
Differentiable
Partitioning
Density estimation
Rate of convergence
Influence

Keywords

  • kernel and nearest neighbor regression estimation
  • kernel density estimation
  • partitioning
  • rate of convergence
  • Regression residual

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Statistics, Probability and Uncertainty

Cite this

Rate of convergence of the density estimation of regression residual. / Györfi, L.; Walk, Harro.

In: Statistics and Risk Modeling, Vol. 30, No. 1, 01.01.2013, p. 55-74.

Research output: Contribution to journalArticle

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