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Licensed Unlicensed Requires Authentication Published by De Gruyter (A) March 6, 2013

Rate of convergence of the density estimation of regression residual

  • László Györfi and Harro Walk


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.

* Correspondence address: Budapest University of Technology and Economics, Dept. of Computer Science and Information Theory, 1521 Stoczek u. 2, Budapest, Ungarn,

Published Online: 2013-03-06
Published in Print: 2013-03

© by Oldenbourg Wissenschaftsverlag, München, Germany

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