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The Hilbert Kernel Regression Estimate

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  • Devroye, Luc
  • Györfi, Laszlo
  • Krzyzak, Adam

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.

Suggested Citation

  • Devroye, Luc & Györfi, Laszlo & Krzyzak, Adam, 1998. "The Hilbert Kernel Regression Estimate," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 209-227, May.
    • Handle: RePEc:eee:jmvana:v:65:y:1998:i:2:p:209-227
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    References listed on IDEAS

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    1. Marta Horvath & Gábor Lugosi, 1996. "A data-dependent skeleton estimate and a scale-sensitive dimension for classification," Economics Working Papers 199, Department of Economics and Business, Universitat Pompeu Fabra.
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    1. Devroye, Luc & Krzyzak, Adam, 1999. "On the Hilbert kernel density estimate," Statistics & Probability Letters, Elsevier, vol. 44(3), pages 299-308, September.
    2. Devroye, Luc & Krzyzak, Adam, 2002. "New Multivariate Product Density Estimators," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 88-110, July.

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