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Composite quantile estimation in partial functional linear regression model with dependent errors

  • Ping Yu
  • Ting Li
  • Zhongyi ZhuEmail author
  • Zhongzhan Zhang


In this paper, we consider composite quantile estimation for the partial functional linear regression model with errors from a short-range dependent and strictly stationary linear processes. The functional principal component analysis method is employed to estimate the slope function and the functional predictive variable, respectively. Under some regularity conditions, we obtain the optimal convergence rate of the slope function, and the asymptotic normality of the parameter vector. Simulation studies demonstrate that the proposed new estimation method is robust and works much better than the least squares based method when there are outliers in the dataset or the autoregressive error distribution follows a heavy-tailed distribution. Finally, we apply the proposed methodology to electricity consumption data.


Composite quantile estimation Functional principal component analysis Functional linear regression model Short-range dependence Strictly stationary 

Mathematics Subject Classification

62G08 62G20 



This work was supported by National Natural Science Foundation of China (Grant Nos. 11671096, 11690013, 11731011, 11771032).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Ping Yu
    • 1
    • 2
  • Ting Li
    • 1
  • Zhongyi Zhu
    • 1
    Email author
  • Zhongzhan Zhang
    • 3
  1. 1.Department of StatisticsFudan UniversityShanghaiChina
  2. 2.School of Mathematics and Computer ScienceShanxi Normal UniversityLinfenChina
  3. 3.College of Applied SciencesBeijing University of TechnologyBeijingChina

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