A Comprehensive Analysis of MSE in Estimating Conditional Hazard Functions: A Local Linear, Single Index Approach for MAR Scenarios
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...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-02-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/12/3/495 |
| _version_ | 1797318456510513152 |
|---|---|
| author | Abderrahmane Belguerna Hamza Daoudi Khadidja Abdelhak Boubaker Mechab Zouaoui Chikr Elmezouar Fatimah Alshahrani |
| author_facet | Abderrahmane Belguerna Hamza Daoudi Khadidja Abdelhak Boubaker Mechab Zouaoui Chikr Elmezouar Fatimah Alshahrani |
| author_sort | Abderrahmane Belguerna |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-08T03:52:39Z |
| format | Article |
| id | doaj.art-577453d39ca542bc8c01c5df42ebc20a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-08T03:52:39Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-577453d39ca542bc8c01c5df42ebc20a2024-02-09T15:18:33ZengMDPI AGMathematics2227-73902024-02-0112349510.3390/math12030495A Comprehensive Analysis of MSE in Estimating Conditional Hazard Functions: A Local Linear, Single Index Approach for MAR ScenariosAbderrahmane Belguerna0Hamza Daoudi1Khadidja Abdelhak2Boubaker Mechab3Zouaoui Chikr Elmezouar4Fatimah Alshahrani5Department of Mathematics, Sciences Institute, S.A University Center, P.O. Box 66, Naama 45000, AlgeriaDepartment of Electrical Engineering, College of Technology, Tahri Mohamed University, Al-Qanadisa Road, P.O. Box 417, Bechar 08000, AlgeriaDepartment of Mathematics, Sciences Institute, S.A University Center, P.O. Box 66, Naama 45000, AlgeriaLaboratory of Statistics and Stochastic Processes, University of Djillali Liabes, P.O. Box 89, Sidi Bel Abbes 22000, 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 ArabiaIn 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.https://www.mdpi.com/2227-7390/12/3/495local polynomial methodconditional hazard estimationmissing at randomsingle index modelmean squared error |
| spellingShingle | Abderrahmane Belguerna Hamza Daoudi Khadidja Abdelhak Boubaker Mechab Zouaoui Chikr Elmezouar Fatimah Alshahrani A Comprehensive Analysis of MSE in Estimating Conditional Hazard Functions: A Local Linear, Single Index Approach for MAR Scenarios Mathematics local polynomial method conditional hazard estimation missing at random single index model mean squared error |
| title | A Comprehensive Analysis of MSE in Estimating Conditional Hazard Functions: A Local Linear, Single Index Approach for MAR Scenarios |
| title_full | A Comprehensive Analysis of MSE in Estimating Conditional Hazard Functions: A Local Linear, Single Index Approach for MAR Scenarios |
| title_fullStr | A Comprehensive Analysis of MSE in Estimating Conditional Hazard Functions: A Local Linear, Single Index Approach for MAR Scenarios |
| title_full_unstemmed | A Comprehensive Analysis of MSE in Estimating Conditional Hazard Functions: A Local Linear, Single Index Approach for MAR Scenarios |
| title_short | A Comprehensive Analysis of MSE in Estimating Conditional Hazard Functions: A Local Linear, Single Index Approach for MAR Scenarios |
| title_sort | comprehensive analysis of mse in estimating conditional hazard functions a local linear single index approach for mar scenarios |
| topic | local polynomial method conditional hazard estimation missing at random single index model mean squared error |
| url | https://www.mdpi.com/2227-7390/12/3/495 |
| work_keys_str_mv | AT abderrahmanebelguerna acomprehensiveanalysisofmseinestimatingconditionalhazardfunctionsalocallinearsingleindexapproachformarscenarios AT hamzadaoudi acomprehensiveanalysisofmseinestimatingconditionalhazardfunctionsalocallinearsingleindexapproachformarscenarios AT khadidjaabdelhak acomprehensiveanalysisofmseinestimatingconditionalhazardfunctionsalocallinearsingleindexapproachformarscenarios AT boubakermechab acomprehensiveanalysisofmseinestimatingconditionalhazardfunctionsalocallinearsingleindexapproachformarscenarios AT zouaouichikrelmezouar acomprehensiveanalysisofmseinestimatingconditionalhazardfunctionsalocallinearsingleindexapproachformarscenarios AT fatimahalshahrani acomprehensiveanalysisofmseinestimatingconditionalhazardfunctionsalocallinearsingleindexapproachformarscenarios AT abderrahmanebelguerna comprehensiveanalysisofmseinestimatingconditionalhazardfunctionsalocallinearsingleindexapproachformarscenarios AT hamzadaoudi comprehensiveanalysisofmseinestimatingconditionalhazardfunctionsalocallinearsingleindexapproachformarscenarios AT khadidjaabdelhak comprehensiveanalysisofmseinestimatingconditionalhazardfunctionsalocallinearsingleindexapproachformarscenarios AT boubakermechab comprehensiveanalysisofmseinestimatingconditionalhazardfunctionsalocallinearsingleindexapproachformarscenarios AT zouaouichikrelmezouar comprehensiveanalysisofmseinestimatingconditionalhazardfunctionsalocallinearsingleindexapproachformarscenarios AT fatimahalshahrani comprehensiveanalysisofmseinestimatingconditionalhazardfunctionsalocallinearsingleindexapproachformarscenarios |