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Rates of convergence for partitioning and nearest neighbor regression estimates with unbounded data

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  • Kohler, Michael
  • Krzyzak, Adam
  • Walk, Harro
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    Abstract

    Estimation of regression functions from independent and identically distributed data is considered. The L2 error with integration with respect to the design measure is used as an error criterion. Usually in the analysis of the rate of convergence of estimates besides smoothness assumptions on the regression function and moment conditions on Y also boundedness assumptions on X are made. In this article we consider partitioning and nearest neighbor estimates and show that by replacing the boundedness assumption on X by a proper moment condition the same rate of convergence can be shown as for bounded data.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 97 (2006)
    Issue (Month): 2 (February)
    Pages: 311-323

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    Handle: RePEc:eee:jmvana:v:97:y:2006:i:2:p:311-323

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    Related research

    Keywords: Regression Partitioning estimate Nearest neighbor estimate Rate of convergence;

    References

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    1. Györfi, László & Walk, Harro, 1997. "On the strong universal consistency of a recursive regression estimate by Pál Révész," Statistics & Probability Letters, Elsevier, vol. 31(3), pages 177-183, January.
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    Cited by:
    1. Sancetta, A., 2007. "Online Forecast Combination for Dependent Heterogeneous Data," Cambridge Working Papers in Economics 0718, Faculty of Economics, University of Cambridge.
    2. Liitiäinen, Elia & Corona, Francesco & Lendasse, Amaury, 2010. "Residual variance estimation using a nearest neighbor statistic," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 811-823, April.
    3. Kohler, Michael & Krzyżak, Adam, 2013. "Optimal global rates of convergence for interpolation problems with random design," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1871-1879.
    4. Cattaneo, Matias D. & Farrell, Max H., 2013. "Optimal convergence rates, Bahadur representation, and asymptotic normality of partitioning estimators," Journal of Econometrics, Elsevier, vol. 174(2), pages 127-143.

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