The Hilbert Kernel Regression Estimate

Luc Devroye, Laszlo Györfi and Adam Krzyzak

Journal of Multivariate Analysis, 1998, vol. 65, issue 2, 209-227

Abstract: Let (X, 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.

Keywords: regression function estimation; kernel estimate; convergence; bandwidth selection; Nadaraya-Watson estimate; nonparametric estimation (search for similar items in EconPapers)
Date: 1998
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