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The consistency and asymptotic normality of the kernel type expectile regression estimator for functional data

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  • Mohammedi, Mustapha
  • Bouzebda, Salim
  • Laksaci, Ali

Abstract

The aim of this paper is to nonparametrically estimate the expectile regression in the case of a functional predictor and a scalar response. More precisely, we construct a kernel-type estimator of the expectile regression function. The main contribution of this study is the establishment of the asymptotic properties of the expectile regression estimator. Precisely, we establish the almost complete convergence with rate. Furthermore, we obtain the asymptotic normality of the proposed estimator under some mild conditions. We provide how to apply our results to construct the confidence intervals. The case of functional predictor is of particular interest and challenge, both from theoretical as well as practical point of view. We discuss the potential impacts of functional expectile regression in NFDA with a particular focus on the supervised classification, prediction and financial risk analysis problems. Finally, the finite-sample performances of the model and the estimation method are illustrated using the analysis of simulated data and real data coming from the financial risk analysis.

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  • Mohammedi, Mustapha & Bouzebda, Salim & Laksaci, Ali, 2021. "The consistency and asymptotic normality of the kernel type expectile regression estimator for functional data," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:jmvana:v:181:y:2021:i:c:s0047259x20302542
    DOI: 10.1016/j.jmva.2020.104673
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    Cited by:

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    2. Salim Bouzebda & Amel Nezzal & Tarek Zari, 2022. "Uniform Consistency for Functional Conditional U -Statistics Using Delta-Sequences," Mathematics, MDPI, vol. 11(1), pages 1-39, December.
    3. Sultana Didi & Salim Bouzebda, 2022. "Wavelet Density and Regression Estimators for Continuous Time Functional Stationary and Ergodic Processes," Mathematics, MDPI, vol. 10(22), pages 1-37, November.
    4. Litimein, Ouahiba & Laksaci, Ali & Mechab, Boubaker & Bouzebda, Salim, 2023. "Local linear estimate of the functional expectile regression," Statistics & Probability Letters, Elsevier, vol. 192(C).
    5. Salim Bouzebda & Inass Soukarieh, 2022. "Non-Parametric Conditional U -Processes for Locally Stationary Functional Random Fields under Stochastic Sampling Design," Mathematics, MDPI, vol. 11(1), pages 1-69, December.
    6. 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.
    7. 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).
    8. 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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