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Nonparametric M-regression for functional ergodic data

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  • Gheriballah, Abdelkader
  • Laksaci, Ali
  • Sekkal, Soumeya

Abstract

Let (Xi,Yi)i=1,…,n be a sequence of stationary ergodic processes valued in F×R, where F is a semi-metric space. We consider the problem of estimating the regression function of Yi given Xi by the robust M-estimation method. The principal aim of this work is to prove the almost complete convergence (with rate) for the proposed estimator. This result is obtained under a stationary ergodic process assumption, without using traditional mixing conditions.

Suggested Citation

  • Gheriballah, Abdelkader & Laksaci, Ali & Sekkal, Soumeya, 2013. "Nonparametric M-regression for functional ergodic data," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 902-908.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:3:p:902-908
    DOI: 10.1016/j.spl.2012.12.004
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    References listed on IDEAS

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    11. K. Benhenni & F. Ferraty & M. Rachdi & P. Vieu, 2007. "Local smoothing regression with functional data," Computational Statistics, Springer, vol. 22(3), pages 353-369, September.
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    Cited by:

    1. Somia Ayad & Ali Laksaci & Saâdia Rahmani & Rachida Rouane, 2020. "On the local linear modelization of the conditional density for functional and ergodic data," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 237-254, August.
    2. Kamal Boukhetala & Jean-François Dupuy, 2019. "Modélisation Stochastique et Statistique Book of Proceedings," Post-Print hal-02593238, HAL.
    3. Fatimah Alshahrani & Ibrahim M. Almanjahie & Zouaoui Chikr Elmezouar & Zoulikha Kaid & Ali Laksaci & Mustapha Rachdi, 2022. "Functional Ergodic Time Series Analysis Using Expectile Regression," Mathematics, MDPI, vol. 10(20), pages 1-17, October.
    4. Saliha Derrar & Ali Laksaci & Elias Ould Saïd, 2020. "M-estimation of the regression function under random left truncation and functional time series model," Statistical Papers, Springer, vol. 61(3), pages 1181-1202, June.
    5. 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.

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