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Regression models with correlated errors based on functional random design

Author

Listed:
  • Karim Benhenni

    (Université Grenoble Alpes)

  • Sonia Hedli-Griche

    (Université Sétif)

  • Mustapha Rachdi

    (Université Grenoble Alpes)

Abstract

This paper deals with the study of the estimation of the functional regression operator when the explanatory variable takes its values in some abstract space of functions. The main goal of this paper is to establish the exact rate of convergence of the mean squared error of the functional version of the Nadaraya–Watson kernel estimator when the errors come from a stationary process under long or short memory and based on random functional data. Moreover, these theoretical results are checked through some simulations with regular (smooth) and irregular curves and then with real data.

Suggested Citation

  • Karim Benhenni & Sonia Hedli-Griche & Mustapha Rachdi, 2017. "Regression models with correlated errors based on functional random design," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 1-21, March.
    • Handle: RePEc:spr:testjl:v:26:y:2017:i:1:d:10.1007_s11749-016-0495-1
    DOI: 10.1007/s11749-016-0495-1
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    References listed on IDEAS

    as
    1. 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.
    2. Benhenni, K. & Hedli-Griche, S. & Rachdi, M., 2010. "Estimation of the regression operator from functional fixed-design with correlated errors," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 476-490, February.
    3. Roussas, G. G., 1994. "Asymptotic Normality of Random Fields of Positively or Negatively Associated Processes," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 152-173, July.
    4. Frédéric Ferraty & Philippe Vieu, 2002. "The Functional Nonparametric Model and Application to Spectrometric Data," Computational Statistics, Springer, vol. 17(4), pages 545-564, December.
    5. Masry, Elias, 2005. "Nonparametric regression estimation for dependent functional data: asymptotic normality," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 155-177, January.
    6. Rachdi, Mustapha & Laksaci, Ali & Demongeot, Jacques & Abdali, Abdel & Madani, Fethi, 2014. "Theoretical and practical aspects of the quadratic error in the local linear estimation of the conditional density for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 53-68.
    7. Benhenni, K. & Hedli-Griche, S. & Rachdi, M. & Vieu, P., 2008. "Consistency of the regression estimator with functional data under long memory conditions," Statistics & Probability Letters, Elsevier, vol. 78(8), pages 1043-1049, June.
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    Cited by:

    1. M. D. Ruiz-Medina & D. Miranda & R. M. Espejo, 2019. "Dynamical multiple regression in function spaces, under kernel regressors, with ARH(1) errors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 943-968, September.
    2. Benhenni, Karim & Hassan, Ali Hajj & Su, Yingcai, 2019. "Local polynomial estimation of regression operators from functional data with correlated errors," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 80-94.
    3. Karim Benhenni & Ali Hajj Hassan & Yingcai Su, 2024. "The effect of correlated errors on the performance of local linear estimation of regression function based on random functional design," Statistical Papers, Springer, vol. 65(6), pages 3395-3423, August.
    4. Lihong Wang, 2020. "Nearest neighbors estimation for long memory functional data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(4), pages 709-725, December.

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