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

Author

Listed:
  • Ping Yu

    (Fudan University
    Shanxi Normal University)

  • Zhongyi Zhu

    (Fudan University)

  • Zhongzhan Zhang

    (Beijing University of Technology)

Abstract

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.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:34:y:2019:i:2:d:10.1007_s00180-018-0810-2
    DOI: 10.1007/s00180-018-0810-2
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Yu, Ping & Song, Xinyuan & Du, Jiang, 2024. "Composite expectile estimation in partial functional linear regression model," Journal of Multivariate Analysis, Elsevier, vol. 203(C).
    3. Germán Aneiros & Ricardo Cao & Philippe Vieu, 2019. "Editorial on the special issue on Functional Data Analysis and Related Topics," Computational Statistics, Springer, vol. 34(2), pages 447-450, June.

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