The Hilbert Kernel Regression Estimate

Let (X,Â Y) be an d--valued regression pair, whereXhas a density andYis bounded. Ifni.i.d. samples are drawn from this distribution, the Nadaraya-Watson kernel regression estimate in dwith Hilbert kernelK(x)=1/||x||dis shown to converge weakly for all such regression pairs. We also show that strong convergence cannot be obtained. This is particularly interesting as this regression estimate does not have a smoothing parameter.

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Year of publication:	1998
Authors:	Devroye, Luc ; Györfi, Laszlo ; Krzyzak, Adam
Published in:	Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 65.1998, 2, p. 209-227
Publisher:	Elsevier
Subject:	regression function estimation \| kernel estimate \| convergence \| bandwidth selection \| Nadaraya-Watson estimate \| nonparametric estimation

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005106960