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Robust Estimation of L 1 -Modal Regression Under Functional Single-Index Models for Practical Applications

Author

Listed:
  • Fatimah A. Almulhim

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Mohammed B. Alamari

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

  • Salim Bouzebda

    (Laboratoire de Mathématiques Appliquées de Compiègne (L.M.A.C.), Université de Technologie de Compiègne, 60200 Compiègne, 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)

Abstract

We propose a robust procedure to estimate the conditional mode of a univariate outcome O given a Hilbertian explanatory variable I , under the assumption that ( O , I ) follow a single-index structure. The estimator is constructed using the M -estimator for the conditional density, and we establish its complete convergence. We discuss the estimator’s advantages in addressing challenges within functional data analysis, particularly robustness and reliability. We then evaluate both the performance and practical implementation of our method via Monte Carlo simulations. Furthermore, we carry out an empirical study to showcase the improved reliability and robustness of this estimator compared to conventional approaches. In particular, our methodology is applied to predict fuel quality based on spectrometry data, illustrating its strong potential in real-world scenarios.

Suggested Citation

  • Fatimah A. Almulhim & Mohammed B. Alamari & Salim Bouzebda & Zoulikha Kaid & Ali Laksaci, 2025. "Robust Estimation of L 1 -Modal Regression Under Functional Single-Index Models for Practical Applications," Mathematics, MDPI, vol. 13(4), pages 1-20, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:4:p:602-:d:1589615
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    References listed on IDEAS

    as
    1. Demongeot, Jacques & Hamie, Ali & Laksaci, Ali & Rachdi, Mustapha, 2016. "Relative-error prediction in nonparametric functional statistics: Theory and practice," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 261-268.
    2. M’hamed Ezzahrioui & Elias Ould Saïd, 2022. "On the robust regression for a censored response data in the single functional index model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(15), pages 5162-5186, June.
    3. Zhou, Weilun & Gao, Jiti & Harris, David & Kew, Hsein, 2024. "Semi-parametric single-index predictive regression models with cointegrated regressors," Journal of Econometrics, Elsevier, vol. 238(1).
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    8. Mustapha Mohammedi & Salim Bouzebda & Ali Laksaci & Oussama Bouanani, 2024. "Asymptotic normality of the k-NN single index regression estimator for functional weak dependence data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(9), pages 3143-3168, May.
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