The Hilbert Kernel Regression Estimate
AbstractLet (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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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 65 (1998)
Issue (Month): 2 (May)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- Devroye, Luc & Krzyzak, Adam, 2002. "New Multivariate Product Density Estimators," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 88-110, July.
- Devroye, Luc & Krzyzak, Adam, 1999. "On the Hilbert kernel density estimate," Statistics & Probability Letters, Elsevier, vol. 44(3), pages 299-308, September.
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