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Strongly consistent density estimation of the regression residual

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  • Györfi, László
  • Walk, Harro
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    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. For heteroscedastic regression, we prove the strong universal (density-free) L1-consistency of a recursive and a nonrecursive kernel density estimate based on a regression estimate.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212002556
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 11 ()
    Pages: 1923-1929

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:11:p:1923-1929

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    Related research

    Keywords: Regression residual; Nonparametric kernel density estimation; Nonparametric regression estimation; Heteroscedastic regression;

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