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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Main Authors: Said Attaoui, Oum Elkheir Benouda, Salim Bouzebda, Ali Laksaci
Format: Article
Language:English
Published: MDPI AG 2025-03-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/5/886
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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.
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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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