盖玉洁, 孟康, 谢雨娇, 王晓迪. 部分线性回归模型的可更新估计方法[J]. 应用概率统计, 2026, 42(1): 131-156. DOI: 10.12460/j.issn.1001-4268.aps.2026.2024058
引用本文: 盖玉洁, 孟康, 谢雨娇, 王晓迪. 部分线性回归模型的可更新估计方法[J]. 应用概率统计, 2026, 42(1): 131-156. DOI: 10.12460/j.issn.1001-4268.aps.2026.2024058
GAI Yujie, MENG Kang, XIE Yujiao, WANG Xiaodi, . A Renewable Estimation Method for Partially Linear Regression Models[J]. Chinese Journal of Applied Probability and Statistics, 2026, 42(1): 131-156.
Citation: GAI Yujie, MENG Kang, XIE Yujiao, WANG Xiaodi, . A Renewable Estimation Method for Partially Linear Regression Models[J]. Chinese Journal of Applied Probability and Statistics, 2026, 42(1): 131-156.

部分线性回归模型的可更新估计方法

A Renewable Estimation Method for Partially Linear Regression Models

  • 摘要: 本文提出了部分线性回归模型的可更新估计方法, 在传统的正则条件下, 证明了可更新参数估计的相合性和渐近正态性以及可更新非参数估计的性质. 此外, 本文还对可更新估计计算效率进行了说明, 当每块数据样本数小于数据块的数量时, 与全数据集估计相比, 可更新估计可以显著减少估计所用时间. 最后,通过数值模拟验证了所提出方法的优越性, 并使用可更新估计方法对空气质量数据进行了分析.

     

    Abstract: In this paper, we implement renewable estimation for partially linear regression models. Under traditional regularity conditions, the consistency and asymptotic normality of the renewable parameter estimation are established, as well as the properties of renewable nonparametric estimations. In addition, we demonstrate the computational efficiency of the renewable estimations, showing that when the sample size per block is smaller than the number of data blocks, our method can significantly reduce the estimation time compared to the estimation using the full dataset. We conduct simulation experiments to demonstrate the superiority and the efficiency of the proposed procedure, and apply the renewable estimation method to analyze the air quality data.

     

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