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Strongly consistent density estimation of the regression residual

László Györfi and Harro Walk

Statistics & Probability Letters, 2012, vol. 82, issue 11, 1923-1929

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.

Keywords: Regression residual; Nonparametric kernel density estimation; Nonparametric regression estimation; Heteroscedastic regression (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spl.2012.06.021

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