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Consistent nonparametric regression from recursive partitioning schemes

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  • Gordon, Louis
  • Olshen, Richard A.

Abstract

We here extend our results on asymptotically Bayes risk efficient classification to the general regression scenario. More precisely, we find Lp consistent estimators for an arbitrary regression function provided only that the dependent variable has a finite absolute pth moment. The estimators are truncated and untruncated local means derived from recursive partitioning schemes.

Suggested Citation

  • Gordon, Louis & Olshen, Richard A., 1980. "Consistent nonparametric regression from recursive partitioning schemes," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 611-627, December.
    • Handle: RePEc:eee:jmvana:v:10:y:1980:i:4:p:611-627
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    Citations

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    Cited by:

    1. Lu Lin & Feng Li, 2008. "Stable and bias-corrected estimation for nonparametric regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(4), pages 283-303.
    2. Biau, Gérard & Devroye, Luc & Dujmović, Vida & Krzyżak, Adam, 2012. "An affine invariant k-nearest neighbor regression estimate," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 24-34.
    3. Zhang, Heping, 2004. "Recursive Partitioning and Tree-based Methods," Papers 2004,30, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    4. Levon Demirdjian & Majid Mojirsheibani, 2019. "Kernel classification with missing data and the choice of smoothing parameters," Statistical Papers, Springer, vol. 60(5), pages 1487-1513, October.
    5. Luis Sanguiao Sande & Li-Chun Zhang, 2021. "Design-Unbiased Statistical Learning in Survey Sampling," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 714-744, August.

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