On the Exact Asymptotic Error of the Kernel Estimator of the Conditional Hazard Function for Quasi-Associated Functional Variables
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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">&...
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2025-07-01
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| author | Abdelkader Rassoul Abderrahmane Belguerna Hamza Daoudi Zouaoui Chikr Elmezouar Fatimah Alshahrani |
| author_facet | Abdelkader Rassoul Abderrahmane Belguerna Hamza Daoudi Zouaoui Chikr Elmezouar Fatimah Alshahrani |
| author_sort | Abdelkader Rassoul |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow><mo>(</mo><msub><mi>U</mi><mi>n</mi></msub><mo>)</mo></mrow><mrow><mi>n</mi><mo>∈</mo><mi mathvariant="double-struck">N</mi></mrow></msub></semantics></math></inline-formula> 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. |
| format | Article |
| id | doaj-art-6de3018cd2bb42e5b31abd7086d63808 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-6de3018cd2bb42e5b31abd7086d638082025-08-20T03:50:17ZengMDPI AGMathematics2227-73902025-07-011313217210.3390/math13132172On the Exact Asymptotic Error of the Kernel Estimator of the Conditional Hazard Function for Quasi-Associated Functional VariablesAbdelkader Rassoul0Abderrahmane Belguerna1Hamza Daoudi2Zouaoui Chikr Elmezouar3Fatimah Alshahrani4Department of Mathematics, Science Institute, Salhi Ahmed University Center of Naama, P.O. Box 66, Naama 45000, AlgeriaDepartment of Mathematics, Science Institute, Salhi Ahmed University Center of Naama, P.O. Box 66, Naama 45000, AlgeriaLaboratory of Mathematics, Statistics and Computer Science for Scientific Research (W1550900), Salhi Ahmed University Center of Naama, P.O. Box 66, Naama 45000, AlgeriaDepartment of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi ArabiaDepartment of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaThe 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow><mo>(</mo><msub><mi>U</mi><mi>n</mi></msub><mo>)</mo></mrow><mrow><mi>n</mi><mo>∈</mo><mi mathvariant="double-struck">N</mi></mrow></msub></semantics></math></inline-formula> 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.https://www.mdpi.com/2227-7390/13/13/2172conditional hazard functionkernel estimationasymptotic errorquasi-associated data |
| spellingShingle | Abdelkader Rassoul Abderrahmane Belguerna Hamza Daoudi Zouaoui Chikr Elmezouar Fatimah Alshahrani On the Exact Asymptotic Error of the Kernel Estimator of the Conditional Hazard Function for Quasi-Associated Functional Variables Mathematics conditional hazard function kernel estimation asymptotic error quasi-associated data |
| title | On the Exact Asymptotic Error of the Kernel Estimator of the Conditional Hazard Function for Quasi-Associated Functional Variables |
| title_full | On the Exact Asymptotic Error of the Kernel Estimator of the Conditional Hazard Function for Quasi-Associated Functional Variables |
| title_fullStr | On the Exact Asymptotic Error of the Kernel Estimator of the Conditional Hazard Function for Quasi-Associated Functional Variables |
| title_full_unstemmed | On the Exact Asymptotic Error of the Kernel Estimator of the Conditional Hazard Function for Quasi-Associated Functional Variables |
| title_short | On the Exact Asymptotic Error of the Kernel Estimator of the Conditional Hazard Function for Quasi-Associated Functional Variables |
| title_sort | on the exact asymptotic error of the kernel estimator of the conditional hazard function for quasi associated functional variables |
| topic | conditional hazard function kernel estimation asymptotic error quasi-associated data |
| url | https://www.mdpi.com/2227-7390/13/13/2172 |
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