Strongly Consistent Density Estimation of Regression Redidual

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Date
2012MFO Scientific Program
Research in Pairs 2012Series
Oberwolfach Preprints;2012,07Author
Györfi, László
Walk, Harro
Metadata
Show full item recordOWP-2012-07
Abstract
Consider the regression problem with a response variable $Y$ and with a $d$-dimensional feature vector $X$. For the regression function $m(x) = \mathbb{E}\{Y|X = x\}$, 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) $L_1$-consistency of a recursive and a nonrecursive kernel density estimate based on a regression estimate.