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

Abdelkader Rassoul, Abderrahmane Belguerna, Hamza Daoudi (), Zouaoui Chikr Elmezouar and Fatimah Alshahrani
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Abdelkader Rassoul: Department of Mathematics, Science Institute, 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
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
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, 2025, vol. 13, issue 13, 1-27

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.

Keywords: conditional hazard function; kernel estimation; asymptotic error; quasi-associated data (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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