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On the Exact Asymptotic Error of the Kernel Estimator of the Conditional Hazard Function for Quasi-Associated Functional Variables

Author

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  • Abdelkader Rassoul

    (Department of Mathematics, Science Institute, Salhi Ahmed University Center of Naama, P.O. Box 66, Naama 45000, Algeria
    Laboratory of Mathematics, Statistics and Computer Science for Scientific Research (W1550900), Salhi Ahmed University Center of Naama, P.O. Box 66, Naama 45000, Algeria)

  • Abderrahmane Belguerna

    (Department of Mathematics, Science Institute, Salhi Ahmed University Center of Naama, P.O. Box 66, Naama 45000, Algeria
    Laboratory of Mathematics, Statistics and Computer Science for Scientific Research (W1550900), Salhi Ahmed University Center of Naama, P.O. Box 66, Naama 45000, Algeria)

  • Hamza Daoudi

    (Laboratory of Mathematics, Statistics and Computer Science for Scientific Research (W1550900), Salhi Ahmed University Center of Naama, P.O. Box 66, Naama 45000, Algeria
    Department of Electrical Engineering, College of Technology, Tahri Mohamed University, Al-Qanadisa Road, P.O. Box 417, Bechar 08000, Algeria)

  • Zouaoui Chikr Elmezouar

    (Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia)

  • Fatimah Alshahrani

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

Abstract

The goal of this research is to analyze the mean squared error (MSE) of the kernel estimator for the conditional hazard rate, assuming that the sequence of real random vector variables ( U n ) n ∈ N satisfies the quasi-association condition. By employing kernel smoothing techniques and asymptotic analysis, we derive the exact asymptotic expression for the leading terms of the quadratic error, providing a precise characterization of the estimator’s convergence behavior. In addition to the theoretical derivations and a controlled simulation study that validates the asymptotic properties, this work includes a real-data application involving monthly unemployment rates in the United States from 1948 to 2025. The comparison between the estimated and observed values confirms the relevance and robustness of the proposed method in a practical economic context. This study thus extends existing results on hazard rate estimation by addressing more complex dependence structures and by demonstrating the applicability of the methodology to real functional data, thereby contributing to both the theoretical development and empirical deployment of kernel-based methods in survival and labor market analysis.

Suggested Citation

  • Abdelkader Rassoul & Abderrahmane Belguerna & Hamza Daoudi & Zouaoui Chikr Elmezouar & Fatimah Alshahrani, 2025. "On the Exact Asymptotic Error of the Kernel Estimator of the Conditional Hazard Function for Quasi-Associated Functional Variables," Mathematics, MDPI, vol. 13(13), pages 1-27, July.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:13:p:2172-:d:1693827
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    References listed on IDEAS

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    1. Abderrahmane Belguerna & Hamza Daoudi & Khadidja Abdelhak & Boubaker Mechab & Zouaoui Chikr Elmezouar & Fatimah Alshahrani, 2024. "A Comprehensive Analysis of MSE in Estimating Conditional Hazard Functions: A Local Linear, Single Index Approach for MAR Scenarios," Mathematics, MDPI, vol. 12(3), pages 1-20, February.
    2. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    3. Alejandro Quintela-Del-Río, 2008. "Hazard function given a functional variable: Non-parametric estimation under strong mixing conditions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(5), pages 413-430.
    4. Hamza Daoudi & Zouaoui Chikr Elmezouar & Fatimah Alshahrani, 2023. "Asymptotic Results of Some Conditional Nonparametric Functional Parameters in High-Dimensional Associated Data," Mathematics, MDPI, vol. 11(20), pages 1-24, October.
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