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Nonparametric Estimation of the Expected Shortfall Regression for Quasi-Associated Functional Data

Author

Listed:
  • Larbi Ait-Hennani

    (Department of Statistic and Informatics, IUT, Lille 2 University, Rond-point de l’Europe, BP. 557, F 59060 Roubaix, France)

  • Zoulikha Kaid

    (Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia)

  • Ali Laksaci

    (Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia)

  • Mustapha Rachdi

    (Laboratoire AGEIS EA 7407, Université Grenoble Alpes (France), UFR SHS, BP. 47, CEDEX 09, F 38040 Grenoble, France)

Abstract

In this paper, we study the nonparametric estimation of the expected shortfall regression when the exogenous observation is functional. The constructed estimator is obtained by combining the double kernels estimator of both conditional value at risk and conditional density function. The asymptotic proprieties of this estimator are established under weak dependency condition. Precisely, we assume that the observations are generated from quasi-associated functional time series and we prove the almost complete convergence of the constructed estimator. This asymptotic result is obtained under a standard condition of functional time series analysis. The finite sample performance of this estimator is evaluated using artificial data.

Suggested Citation

  • Larbi Ait-Hennani & Zoulikha Kaid & Ali Laksaci & Mustapha Rachdi, 2022. "Nonparametric Estimation of the Expected Shortfall Regression for Quasi-Associated Functional Data," Mathematics, MDPI, vol. 10(23), pages 1-23, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4508-:d:987723
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    References listed on IDEAS

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    Cited by:

    1. Litimein, Ouahiba & Laksaci, Ali & Mechab, Boubaker & Bouzebda, Salim, 2023. "Local linear estimate of the functional expectile regression," Statistics & Probability Letters, Elsevier, vol. 192(C).
    2. Yanchun Zhao & Mengzhu Zhang & Qian Ni & Xuhui Wang, 2023. "Adaptive Nonparametric Density Estimation with B-Spline Bases," Mathematics, MDPI, vol. 11(2), pages 1-12, January.
    3. Litimein, Ouahiba & Laksaci, Ali & Ait-Hennani, Larbi & Mechab, Boubaker & Rachdi, Mustapha, 2024. "Asymptotic normality of the local linear estimator of the functional expectile regression," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    4. Salim Bouzebda & Boutheina Nemouchi, 2023. "Weak-convergence of empirical conditional processes and conditional U-processes involving functional mixing data," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 33-88, April.

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