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Distributed penalizing function criterion for local polynomial estimation in nonparametric regression with massive data

Author

Listed:
  • Tianqi Sun

    (Shandong University)

  • Weiyu Li

    (Shandong University
    Shandong University)

  • Lu Lin

    (Shandong University
    Shandong University)

Abstract

The selection of bandwidth is one of the most important issues in local polynomial estimation. However, the related researches about data-driven bandwidth selection methodology in combination with divide-and-conquer (DC) strategy have still been rare in the existing literature, which is not feasible to support the application of local polynomial estimation for massive data sets. In this paper, as a development of traditional penalizing function criterion, we propose a distributed penalizing function (DPF) to achieve the selection of optimal bandwidth. The proposed DPF is computationally efficient for massive data sets and is shown to be “globally optimal” in the sense that the minimization of the DPF is asymptotically equivalent to the minimization of the true empirical loss of the averaged function estimator, i.e., the DC estimator. Besides, a novel algorithm is proposed to resolve the selection of bandwidth parameter with imbalance DC strategy. The performance of this DPF is presented in the simulation studies and the real data analysis.

Suggested Citation

  • Tianqi Sun & Weiyu Li & Lu Lin, 2025. "Distributed penalizing function criterion for local polynomial estimation in nonparametric regression with massive data," Statistical Papers, Springer, vol. 66(3), pages 1-26, April.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:3:d:10.1007_s00362-025-01678-x
    DOI: 10.1007/s00362-025-01678-x
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    References listed on IDEAS

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