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The Hilbert Kernel Regression Estimate

✍ Scribed by Luc Devroye; Laszlo Györfi; Adam Krzyżak

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
410 KB
Volume
65
Category
Article
ISSN
0047-259X

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✦ Synopsis

Let (X, Y ) be an R d _R-valued regression pair, where X has a density and Y is bounded. If n i.i.d. samples are drawn from this distribution, the Nadaraya Watson kernel regression estimate in R d with Hilbert kernel K(x)=1Â&x& d is 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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