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Almost surely consistent nonparametric regression from recursive partitioning schemes

Author

Listed:
  • Gordon, Louis
  • Olshen, Richard A.

Abstract

Presented here are results on almost sure convergence of estimators of regression functions subject to certain moment restrictions. Two somewhat different notions of almost sure convergence are studied: unconditional and conditional given a training sample. The estimators are local means derived from certain recursive partitioning schemes.

Suggested Citation

  • Gordon, Louis & Olshen, Richard A., 1984. "Almost surely consistent nonparametric regression from recursive partitioning schemes," Journal of Multivariate Analysis, Elsevier, vol. 15(2), pages 147-163, October.
    • Handle: RePEc:eee:jmvana:v:15:y:1984:i:2:p:147-163
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    Cited by:

    1. Bilton, Penny & Jones, Geoff & Ganesh, Siva & Haslett, Steve, 2017. "Classification trees for poverty mapping," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 53-66.
    2. Hua Jin & Ying Lu & Kaite Stone & Dennis M. Black, 2004. "Alternative Tree-Structured Survival Analysis Based on Variance of Survival Time," Medical Decision Making, , vol. 24(6), pages 670-680, November.
    3. Gábor Lugosi & Andrew B. Nobel, 1998. "Adaptive model selection using empirical complexities," Economics Working Papers 323, Department of Economics and Business, Universitat Pompeu Fabra.
    4. Abhinandan Dalal & Patrick Blobaum & Shiva Kasiviswanathan & Aaditya Ramdas, 2024. "Anytime-Valid Inference for Double/Debiased Machine Learning of Causal Parameters," Papers 2408.09598, arXiv.org, revised Sep 2024.
    5. Zhang, Heping, 2004. "Recursive Partitioning and Tree-based Methods," Papers 2004,30, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    6. Guangyu Wu & Anders Lindquist, 2024. "A non-classical parameterization for density estimation using sample moments," Statistical Papers, Springer, vol. 65(7), pages 4489-4513, September.

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