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The M-estimator for functional linear regression model

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  • Huang, Lele
  • Wang, Huiwen
  • Zheng, Andi

Abstract

This paper considers the M-estimator for slope function in functional linear regression models. We approximate the slope function by minimizing the loss function based explicitly on functional principal components analysis, and the loss function can be chosen according to what we are estimating. Under mild assumptions, the convergence rate of the estimator of infinite dimensional slope function is derived. A simulation study is conducted to illustrate the numerical performance of the proposed M-estimator.

Suggested Citation

  • Huang, Lele & Wang, Huiwen & Zheng, Andi, 2014. "The M-estimator for functional linear regression model," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 165-173.
    • Handle: RePEc:eee:stapro:v:88:y:2014:i:c:p:165-173
    DOI: 10.1016/j.spl.2014.01.016
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    References listed on IDEAS

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    1. Gheriballah, Abdelkader & Laksaci, Ali & Sekkal, Soumeya, 2013. "Nonparametric M-regression for functional ergodic data," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 902-908.
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    7. F. Ferraty & A. Goia & E. Salinelli & P. Vieu, 2013. "Functional projection pursuit regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 293-320, June.
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    9. Aneiros-Pérez, Germán & Vieu, Philippe, 2006. "Semi-functional partial linear regression," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1102-1110, June.
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    Cited by:

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    3. Li, Ting & Song, Xinyuan & Zhang, Yingying & Zhu, Hongtu & Zhu, Zhongyi, 2021. "Clusterwise functional linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    4. Huang, Lele & Zhao, Junlong & Wang, Huiwen & Wang, Siyang, 2016. "Robust shrinkage estimation and selection for functional multiple linear model through LAD loss," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 384-400.

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