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Efficient online estimation for nonparametric regression models with streaming data

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  • Mingxue Quan

    (Renmin University of China)

  • Yonghong Long

    (Renmin University of China)

Abstract

We consider the online estimation problem for nonparametric regression, and first identify two key tasks: updating summary statistics and dynamically tuning parameters. Based on how these tasks interact, we categorize existing methods into two modes. In the first mode, the tasks can be performed independently, while in the second mode, they must be carried out collaboratively. In contrast, the second mode poses greater challenges because the summary statistics rely on tuning parameters, which change continuously as new data arrive and cannot be predetermined. To address this and improve both estimation accuracy and efficiency, we propose a novel online method for the second mode. Our method introduces a static sequence of candidates to serve as the predetermined parameters for future time points, constructs the summary statistics for each candidate, and then updates them in a one-to-one manner. Additionally, an index is designed to dynamically select the candidate closest to the current globally optimal one, and its corresponding summary statistics are employed for real-time estimation. Finally, we analyze the theoretical properties of the proposed method and demonstrate its effectiveness through numerical experiments and a real data analysis.

Suggested Citation

  • Mingxue Quan & Yonghong Long, 2026. "Efficient online estimation for nonparametric regression models with streaming data," Computational Statistics, Springer, vol. 41(4), pages 1-38, June.
    • Handle: RePEc:spr:compst:v:41:y:2026:i:4:d:10.1007_s00180-026-01756-0
    DOI: 10.1007/s00180-026-01756-0
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    References listed on IDEAS

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    1. Chunlei Ke & Yuedong Wang, 2004. "Smoothing Spline Nonlinear Nonparametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1166-1175, December.
    2. Jianqing Fan & Theo Gasser & Irène Gijbels & Michael Brockmann & Joachim Engel, 1997. "Local Polynomial Regression: Optimal Kernels and Asymptotic Minimax Efficiency," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 79-99, March.
    3. Belloni, Alexandre & Chernozhukov, Victor & Chetverikov, Denis & Kato, Kengo, 2015. "Some new asymptotic theory for least squares series: Pointwise and uniform results," Journal of Econometrics, Elsevier, vol. 186(2), pages 345-366.
    4. Mingxue Quan & Zhenhua Lin, 2024. "Optimal One-Pass Nonparametric Estimation Under Memory Constraint," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(545), pages 285-296, January.
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