Asymptotic Results of Some Conditional Nonparametric Functional Parameters in High-Dimensional Associated Data
In this paper, we propose to study the asymptotic properties of some conditional functional parameters, such as the distribution function, the density, and the hazard function, for an explanatory variable with values in a Hilbert space (infinite dimension) and a response variable real in a quasi-ass...
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MDPI AG
2023-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/20/4290 |
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| author | Hamza Daoudi Zouaoui Chikr Elmezouar Fatimah Alshahrani |
| author_facet | Hamza Daoudi Zouaoui Chikr Elmezouar Fatimah Alshahrani |
| author_sort | Hamza Daoudi |
| collection | DOAJ |
| description | In this paper, we propose to study the asymptotic properties of some conditional functional parameters, such as the distribution function, the density, and the hazard function, for an explanatory variable with values in a Hilbert space (infinite dimension) and a response variable real in a quasi-associated dependency framework. We consider the non parametric estimation of the conditional distribution function by the kernel method in the presence of the quasi-associated dependence, and we establish under general hypotheses the almost complete convergence with speed of the estimator built in the associated case. The estimation of the conditional hazard function will be conducted by utilizing the two outcomes of the conditional distribution function and the conditional density. We establish the asymptotic normality of the kernel estimator as the conditional risk function of a properly normalized functional. We explicitly give the asymptotic variance. Simulation studies were conducted to investigate the behavior of the asymptotic property in the context of finite sample data. All the statistical analyses were performed using R software. |
| first_indexed | 2024-03-10T21:05:01Z |
| format | Article |
| id | doaj.art-baa670f23d7a48d58ba901519c374d3b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T21:05:01Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-baa670f23d7a48d58ba901519c374d3b2023-11-19T17:13:54ZengMDPI AGMathematics2227-73902023-10-011120429010.3390/math11204290Asymptotic Results of Some Conditional Nonparametric Functional Parameters in High-Dimensional Associated DataHamza Daoudi0Zouaoui Chikr Elmezouar1Fatimah Alshahrani2Department of Electrical Engineering, College of Technology, Tahri Mohamed University, Bechar 08000, AlgeriaDepartment of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi ArabiaDepartment of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi ArabiaIn this paper, we propose to study the asymptotic properties of some conditional functional parameters, such as the distribution function, the density, and the hazard function, for an explanatory variable with values in a Hilbert space (infinite dimension) and a response variable real in a quasi-associated dependency framework. We consider the non parametric estimation of the conditional distribution function by the kernel method in the presence of the quasi-associated dependence, and we establish under general hypotheses the almost complete convergence with speed of the estimator built in the associated case. The estimation of the conditional hazard function will be conducted by utilizing the two outcomes of the conditional distribution function and the conditional density. We establish the asymptotic normality of the kernel estimator as the conditional risk function of a properly normalized functional. We explicitly give the asymptotic variance. Simulation studies were conducted to investigate the behavior of the asymptotic property in the context of finite sample data. All the statistical analyses were performed using R software.https://www.mdpi.com/2227-7390/11/20/4290distribution functionasymptotic propertyconditional risk functionweak dependencefunctional data |
| spellingShingle | Hamza Daoudi Zouaoui Chikr Elmezouar Fatimah Alshahrani Asymptotic Results of Some Conditional Nonparametric Functional Parameters in High-Dimensional Associated Data Mathematics distribution function asymptotic property conditional risk function weak dependence functional data |
| title | Asymptotic Results of Some Conditional Nonparametric Functional Parameters in High-Dimensional Associated Data |
| title_full | Asymptotic Results of Some Conditional Nonparametric Functional Parameters in High-Dimensional Associated Data |
| title_fullStr | Asymptotic Results of Some Conditional Nonparametric Functional Parameters in High-Dimensional Associated Data |
| title_full_unstemmed | Asymptotic Results of Some Conditional Nonparametric Functional Parameters in High-Dimensional Associated Data |
| title_short | Asymptotic Results of Some Conditional Nonparametric Functional Parameters in High-Dimensional Associated Data |
| title_sort | asymptotic results of some conditional nonparametric functional parameters in high dimensional associated data |
| topic | distribution function asymptotic property conditional risk function weak dependence functional data |
| url | https://www.mdpi.com/2227-7390/11/20/4290 |
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