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

Abderrahmane Belguerna, Hamza Daoudi (), Khadidja Abdelhak, Boubaker Mechab, Zouaoui Chikr Elmezouar and Fatimah Alshahrani
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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

Mathematics, 2024, vol. 12, issue 3, 1-20

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.

Keywords: local polynomial method; conditional hazard estimation; missing at random; single index model; mean squared error (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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