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Spline estimators for semi-functional linear model

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  • Zhou, Jianjun
  • Chen, Min

Abstract

In this paper, we introduce a semi-functional linear model in which a scalar response variable is explained by a linear operator of a random function and a nonparametric function of a real-valued random variable. We study the spline estimators of the functional coefficient and nonparametric function and obtain the rates of convergence of the spline estimators. Finally, we present some simulation results that illustrate the performance of our estimation method.

Suggested Citation

  • Zhou, Jianjun & Chen, Min, 2012. "Spline estimators for semi-functional linear model," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 505-513.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:3:p:505-513
    DOI: 10.1016/j.spl.2011.11.027
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    References listed on IDEAS

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    5. Frédéric Ferraty & Philippe Vieu, 2002. "The Functional Nonparametric Model and Application to Spectrometric Data," Computational Statistics, Springer, vol. 17(4), pages 545-564, December.
    6. Jianhua Z. Huang & Haipeng Shen, 2004. "Functional Coefficient Regression Models for Non‐linear Time Series: A Polynomial Spline Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(4), pages 515-534, December.
    7. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    8. Aneiros-Pérez, Germán & Vieu, Philippe, 2008. "Nonparametric time series prediction: A semi-functional partial linear modeling," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 834-857, May.
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    Cited by:

    1. Usset, Joseph & Staicu, Ana-Maria & Maity, Arnab, 2016. "Interaction models for functional regression," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 317-329.
    2. Liebl, Dominik & Walders, Fabian, 2019. "Parameter regimes in partial functional panel regression," Econometrics and Statistics, Elsevier, vol. 11(C), pages 105-115.
    3. Bin Yang & Min Chen & Tong Su & Jianjun Zhou, 2023. "Robust Estimation for Semi-Functional Linear Model with Autoregressive Errors," Mathematics, MDPI, vol. 11(2), pages 1-14, January.
    4. Boente, Graciela & Salibian-Barrera, Matías & Vena, Pablo, 2020. "Robust estimation for semi-functional linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    5. Centofanti, Fabio & Fontana, Matteo & Lepore, Antonio & Vantini, Simone, 2022. "Smooth LASSO estimator for the Function-on-Function linear regression model," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    6. Ruiyuan Cao & Jiang Du & Jianjun Zhou & Tianfa Xie, 2020. "FPCA-based estimation for generalized functional partially linear models," Statistical Papers, Springer, vol. 61(6), pages 2715-2735, December.
    7. Jianjun Zhou & Zhao Chen & Qingyan Peng, 2016. "Polynomial spline estimation for partial functional linear regression models," Computational Statistics, Springer, vol. 31(3), pages 1107-1129, September.
    8. Ping Yu & Jiang Du & Zhongzhan Zhang, 2020. "Single-index partially functional linear regression model," Statistical Papers, Springer, vol. 61(3), pages 1107-1123, June.
    9. Guochang Wang & Xiang-Nan Feng & Min Chen, 2016. "Functional Partial Linear Single-index Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 261-274, March.
    10. Qing-Yan Peng & Jian-Jun Zhou & Nian-Sheng Tang, 2016. "Varying coefficient partially functional linear regression models," Statistical Papers, Springer, vol. 57(3), pages 827-841, September.
    11. Fanrong Zhao & Baoxue Zhang, 2024. "A U-Statistic for Testing the Lack of Dependence in Functional Partially Linear Regression Model," Mathematics, MDPI, vol. 12(16), pages 1-24, August.

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