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Kernel density regression in the additive model: a B-spline approach

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  • Facheng Li

    (Guizhou University)

  • Huilan Liu

    (Guizhou University)

Abstract

This paper investigates the estimation of the additive model. The nonparametric functions in the model are approximated through B-splines, and the kernel density regression method is employed to estimate the unknown parameters. Moreover, the convergence rate of the proposed approach is established. We conducted numerical experiments and real-world data analysis to validate the theoretical properties of our proposed method. Our numerical findings indicate that our approach offers superior estimation performance compared to several existing methods for the additive model, particularly in the presence of asymmetric, multimodal, or heavy-tailed error distributions.

Suggested Citation

  • Facheng Li & Huilan Liu, 2025. "Kernel density regression in the additive model: a B-spline approach," Statistical Papers, Springer, vol. 66(1), pages 1-23, January.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:1:d:10.1007_s00362-024-01621-6
    DOI: 10.1007/s00362-024-01621-6
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    References listed on IDEAS

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    1. Boente, Graciela & Martínez, Alejandra Mercedes, 2023. "A robust spline approach in partially linear additive models," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    2. Jun Zhang & Bingqing Lin & Yiping Yang, 2022. "Maximum nonparametric kernel likelihood estimation for multiplicative linear regression models," Statistical Papers, Springer, vol. 63(3), pages 885-918, June.
    3. Zhang, Jun & Lin, Bingqing & Zhou, Yan, 2021. "Kernel density estimation for partial linear multivariate responses models," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    4. Horowitz, Joel L. & Lee, Sokbae, 2005. "Nonparametric Estimation of an Additive Quantile Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1238-1249, December.
    5. Lian, Heng, 2012. "Shrinkage estimation for identification of linear components in additive models," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 225-231.
    6. Xue, Lan & Qu, Annie & Zhou, Jianhui, 2010. "Consistent Model Selection for Marginal Generalized Additive Model for Correlated Data," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1518-1530.
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