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Polynomial spline estimation for partial functional linear regression models

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Listed:
  • Jianjun Zhou

    (Yunnan University)

  • Zhao Chen

    (The Pennsylvania State University)

  • Qingyan Peng

    (Yunnan University)

Abstract

Because of its orthogonality, interpretability and best representation, functional principal component analysis approach has been extensively used to estimate the slope function in the functional linear model. However, as a very popular smooth technique in nonparametric/semiparametric regression, polynomial spline method has received little attention in the functional data case. In this paper, we propose the polynomial spline method to estimate a partial functional linear model. Some asymptotic results are established, including asymptotic normality for the parameter vector and the global rate of convergence for the slope function. Finally, we evaluate the performance of our estimation method by some simulation studies.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:31:y:2016:i:3:d:10.1007_s00180-015-0636-0
    DOI: 10.1007/s00180-015-0636-0
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    References listed on IDEAS

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    1. Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
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    Cited by:

    1. Ping Yu & Ting Li & Zhongyi Zhu & Zhongzhan Zhang, 2019. "Composite quantile estimation in partial functional linear regression model with dependent errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(6), pages 633-656, August.
    2. Ping Yu & Zhongyi Zhu & Zhongzhan Zhang, 2019. "Robust exponential squared loss-based estimation in semi-functional linear regression models," Computational Statistics, Springer, vol. 34(2), pages 503-525, June.
    3. Guodong Shan & Yiheng Hou & Baisen Liu, 2020. "Bayesian robust estimation of partially functional linear regression models using heavy-tailed distributions," Computational Statistics, Springer, vol. 35(4), pages 2077-2092, December.
    4. Yu, Ping & Song, Xinyuan & Du, Jiang, 2024. "Composite expectile estimation in partial functional linear regression model," Journal of Multivariate Analysis, Elsevier, vol. 203(C).
    5. Linjuan Zheng & Beiting Liang & Guochang Wang, 2024. "Adaptive slicing for functional slice inverse regression," Statistical Papers, Springer, vol. 65(5), pages 3261-3284, July.

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