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Single-index partially functional linear regression model

Author

Listed:
  • Ping Yu

    (Beijing University of Technology
    Shanxi Normal University)

  • Jiang Du

    (Beijing University of Technology)

  • Zhongzhan Zhang

    (Beijing University of Technology)

Abstract

In this paper, we propose a flexible single-index partially functional linear regression model, which combines single-index model with functional linear regression model. All the unknown functions are estimated by B-spline approximation. Under some mild conditions, the convergence rates and asymptotic normality of the estimators are obtained. Finally, simulation studies and a real data analysis are conducted to investigate the performance of the proposed methodologies.

Suggested Citation

  • Ping Yu & Jiang Du & Zhongzhan Zhang, 2020. "Single-index partially functional linear regression model," Statistical Papers, Springer, vol. 61(3), pages 1107-1123, June.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:3:d:10.1007_s00362-018-0980-6
    DOI: 10.1007/s00362-018-0980-6
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    References listed on IDEAS

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    1. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
    2. Zhou, Jianjun & Chen, Min, 2012. "Spline estimators for semi-functional linear model," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 505-513.
    3. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    4. Stoker, Thomas M, 1986. "Consistent Estimation of Scaled Coefficients," Econometrica, Econometric Society, vol. 54(6), pages 1461-1481, November.
    5. Aneiros-Pérez, Germán & Vieu, Philippe, 2006. "Semi-functional partial linear regression," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1102-1110, June.
    6. Ping Yu & Zhongzhan Zhang & Jiang Du, 2016. "A test of linearity in partial functional linear regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(8), pages 953-969, November.
    7. Germán Aneiros & Philippe Vieu, 2015. "Partial linear modelling with multi-functional covariates," Computational Statistics, Springer, vol. 30(3), pages 647-671, September.
    8. Heng Lian, 2011. "Functional partial linear model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 115-128.
    9. Sanying Feng & Liugen Xue, 2013. "Variable selection for partially varying coefficient single-index model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(12), pages 2637-2652, December.
    10. Zhao, Peixin & Xue, Liugen, 2010. "Variable selection for semiparametric varying coefficient partially linear errors-in-variables models," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1872-1883, September.
    11. Takuma Yoshida & Kanta Naito, 2014. "Asymptotics for penalised splines in generalised additive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(2), pages 269-289, June.
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    Cited by:

    1. Mohamed Alahiane & Idir Ouassou & Mustapha Rachdi & Philippe Vieu, 2022. "High-Dimensional Statistics: Non-Parametric Generalized Functional Partially Linear Single-Index Model," Mathematics, MDPI, vol. 10(15), pages 1-21, July.
    2. Mohamed Alahiane & Idir Ouassou & Mustapha Rachdi & Philippe Vieu, 2021. "Partially Linear Generalized Single Index Models for Functional Data (PLGSIMF)," Stats, MDPI, vol. 4(4), pages 1-21, September.
    3. Zhiqiang Jiang & Zhensheng Huang & Jing Zhang, 2023. "Functional single-index composite quantile regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(5), pages 595-603, July.

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