Limit Theorems for Kernel Regression Estimator for Quasi-Associated Functional Censored Time Series Within Single Index Structure
In this paper, we develop kernel-based estimators for regression functions under a functional single-index model, applied to censored time series data. By capitalizing on the single-index structure, we reduce the dimensionality of the covariate-response relationship, thereby preserving the ability t...
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MDPI AG
2025-03-01
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| Series: | Mathematics |
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| author | Said Attaoui Oum Elkheir Benouda Salim Bouzebda Ali Laksaci |
| author_facet | Said Attaoui Oum Elkheir Benouda Salim Bouzebda Ali Laksaci |
| author_sort | Said Attaoui |
| collection | DOAJ |
| description | In this paper, we develop kernel-based estimators for regression functions under a functional single-index model, applied to censored time series data. By capitalizing on the single-index structure, we reduce the dimensionality of the covariate-response relationship, thereby preserving the ability to capture intricate dependencies while maintaining a relatively parsimonious form. Specifically, our framework utilizes nonparametric kernel estimation within a quasi-association setting to characterize the underlying relationships. Under mild regularity conditions, we demonstrate that these estimators attain both strong uniform consistency and asymptotic normality. Through extensive simulation experiments, we confirm their robust finite-sample performance. Moreover, an empirical examination using intraday Nikkei stock index returns illustrates that the proposed method significantly outperforms traditional nonparametric regression approaches. |
| format | Article |
| id | doaj-art-c274d92b15934d57b2f9058a4776ed72 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-c274d92b15934d57b2f9058a4776ed722025-08-20T02:59:15ZengMDPI AGMathematics2227-73902025-03-0113588610.3390/math13050886Limit Theorems for Kernel Regression Estimator for Quasi-Associated Functional Censored Time Series Within Single Index StructureSaid Attaoui0Oum Elkheir Benouda1Salim Bouzebda2Ali Laksaci3Department of Mathematics, University of Sciences and Technology Mohamed Boudiaf, Oran BP 1505, El Mnaouar-Oran 31000, AlgeriaDepartment of Mathematics, University of Sciences and Technology Mohamed Boudiaf, Oran BP 1505, El Mnaouar-Oran 31000, AlgeriaLMAC (Laboratory of Applied Mathematics of Compiègne), Université de Technologie de Compiègne, CS 60 319-60 203 Compiègne Cedex, 60203 Compiègne, FranceDepartment of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 62529, Saudi ArabiaIn this paper, we develop kernel-based estimators for regression functions under a functional single-index model, applied to censored time series data. By capitalizing on the single-index structure, we reduce the dimensionality of the covariate-response relationship, thereby preserving the ability to capture intricate dependencies while maintaining a relatively parsimonious form. Specifically, our framework utilizes nonparametric kernel estimation within a quasi-association setting to characterize the underlying relationships. Under mild regularity conditions, we demonstrate that these estimators attain both strong uniform consistency and asymptotic normality. Through extensive simulation experiments, we confirm their robust finite-sample performance. Moreover, an empirical examination using intraday Nikkei stock index returns illustrates that the proposed method significantly outperforms traditional nonparametric regression approaches.https://www.mdpi.com/2227-7390/13/5/886kernel regression estimationweak dependence dataquasi-associated variablessingle functional index model |
| spellingShingle | Said Attaoui Oum Elkheir Benouda Salim Bouzebda Ali Laksaci Limit Theorems for Kernel Regression Estimator for Quasi-Associated Functional Censored Time Series Within Single Index Structure Mathematics kernel regression estimation weak dependence data quasi-associated variables single functional index model |
| title | Limit Theorems for Kernel Regression Estimator for Quasi-Associated Functional Censored Time Series Within Single Index Structure |
| title_full | Limit Theorems for Kernel Regression Estimator for Quasi-Associated Functional Censored Time Series Within Single Index Structure |
| title_fullStr | Limit Theorems for Kernel Regression Estimator for Quasi-Associated Functional Censored Time Series Within Single Index Structure |
| title_full_unstemmed | Limit Theorems for Kernel Regression Estimator for Quasi-Associated Functional Censored Time Series Within Single Index Structure |
| title_short | Limit Theorems for Kernel Regression Estimator for Quasi-Associated Functional Censored Time Series Within Single Index Structure |
| title_sort | limit theorems for kernel regression estimator for quasi associated functional censored time series within single index structure |
| topic | kernel regression estimation weak dependence data quasi-associated variables single functional index model |
| url | https://www.mdpi.com/2227-7390/13/5/886 |
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