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The M-estimator for functional linear regression model

Author

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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. Delsol, Laurent & Ferraty, Frédéric & Vieu, Philippe, 2011. "Structural test in regression on functional variables," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 422-447, March.
    2. Berrendero, J.R. & Justel, A. & Svarc, M., 2011. "Principal components for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2619-2634, September.
    3. Gheriballah, Abdelkader & Laksaci, Ali & Sekkal, Soumeya, 2013. "Nonparametric M-regression for functional ergodic data," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 902-908.
    4. 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.
    5. Aneiros-Pérez, Germán & Vieu, Philippe, 2006. "Semi-functional partial linear regression," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1102-1110, June.
    6. Boente, Graciela & Fraiman, Ricardo, 2000. "Kernel-based functional principal components," Statistics & Probability Letters, Elsevier, vol. 48(4), pages 335-345, July.
    7. Kneip A. & Utikal K. J, 2001. "Inference for Density Families Using Functional Principal Component Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 519-542, June.
    8. Peter Hall & Mohammad Hosseini‐Nasab, 2006. "On properties of functional principal components analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 109-126, February.
    9. Germán Aneiros-Pérez & Philippe Vieu, 2013. "Testing linearity in semi-parametric functional data analysis," Computational Statistics, Springer, vol. 28(2), pages 413-434, April.
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    Cited by:

    1. 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.
    2. Gongming Shi & Tianfa Xie & Zhongzhan Zhang, 2020. "Statistical inference for the functional quadratic quantile regression model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(8), pages 937-960, November.
    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).

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