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

Tianqi Sun (), Weiyu Li () and Lu Lin ()
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Tianqi Sun: Shandong University
Weiyu Li: Shandong University
Lu Lin: Shandong University

Statistical Papers, 2025, vol. 66, issue 3, No 10, 26 pages

Abstract: 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.

Keywords: Nonparametric regression; Local polynomial estimator; Bandwidth selection; Massive data; Divide-and-conquer (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00362-025-01678-x

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