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The Hilbert Kernel Regression Estimate


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


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

    1. Minoru Siotani, 1959. "The extreme value of the generalized distances of the individual points in the multivariate normal sample," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 10(3), pages 183-208, September.
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    Cited by:

    1. Devroye, Luc & Krzyzak, Adam, 2002. "New Multivariate Product Density Estimators," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 88-110, July.
    2. 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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