Rate of convergence of the density estimation of regression residual

László 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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Keywords

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

ASJC Scopus subject areas

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

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