Computational Statistics

, Volume 34, Issue 2, pp 503–525 | Cite as

Robust exponential squared loss-based estimation in semi-functional linear regression models

  • Ping Yu
  • Zhongyi ZhuEmail author
  • Zhongzhan Zhang
Original Paper


In this paper, we present a new robust estimation procedure for semi-functional linear regression models by using exponential squared loss. The outstanding advantage of the proposed method is the resulting estimators are more efficient than the least squares estimators in the presence of outliers or heavy-tail error distributions. The slope function and functional predictor variable are approximated by functional principal component basis functions. Under some regularity conditions, we obtain the optimal convergence rate of slope function, and the asymptotic normality of parameter vector and variance estimator. Finally, we investigate the finite sample performance of the proposed method through a simulation study and real data analysis.


Functional data analysis Functional principal component analysis Exponential squared loss Robust estimation 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  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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