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A Comprehensive Analysis of MSE in Estimating Conditional Hazard Functions: A Local Linear, Single Index Approach for MAR Scenarios

Author

Listed:
  • Abderrahmane Belguerna

    (Department of Mathematics, Sciences Institute, S.A University Center, P.O. Box 66, Naama 45000, Algeria)

  • Hamza Daoudi

    (Department of Electrical Engineering, College of Technology, Tahri Mohamed University, Al-Qanadisa Road, P.O. Box 417, Bechar 08000, Algeria)

  • Khadidja Abdelhak

    (Department of Mathematics, Sciences Institute, S.A University Center, P.O. Box 66, Naama 45000, Algeria)

  • Boubaker Mechab

    (Laboratory of Statistics and Stochastic Processes, University of Djillali Liabes, P.O. Box 89, Sidi Bel Abbes 22000, 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

In unveiling the non-parametric estimation of the conditional hazard function through the local linear method, our study yields key insights into the method’s behavior. We present rigorous analyses demonstrating the mean square convergence of the estimator, subject to specific conditions, within the realm of independent observations with missing data. Furthermore, our contributions extend to the derivation of expressions detailing both bias and variance of the estimator. Emphasizing the practical implications, we underscore the applicability of two distinct models discussed in this paper for single index estimation scenarios. These findings not only enhance our understanding of survival analysis methodologies but also provide practitioners with valuable tools for navigating the complexities of missing data in the estimation of conditional hazard functions. Ultimately, our results affirm the robustness of the local linear method in non-parametrically estimating the conditional hazard function, offering a nuanced perspective on its performance in the challenging context of independent observations with missing data.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:3:p:495-:d:1333231
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    References listed on IDEAS

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    4. Baíllo, Amparo & Grané, Aurea, 2009. "Local linear regression for functional predictor and scalar response," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 102-111, January.
    5. A. Berlinet & A. Elamine & A. Mas, 2011. "Local linear regression for functional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(5), pages 1047-1075, October.
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