Limit Theorems for Kernel Regression Estimator for Quasi-Associated Functional Censored Time Series Within Single Index Structure

Said Attaoui, Oum Elkheir Benouda, Salim Bouzebda () and Ali Laksaci
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Said Attaoui: Department of Mathematics, University of Sciences and Technology Mohamed Boudiaf, Oran BP 1505, El Mnaouar-Oran 31000, Algeria
Oum Elkheir Benouda: Department of Mathematics, University of Sciences and Technology Mohamed Boudiaf, Oran BP 1505, El Mnaouar-Oran 31000, Algeria
Salim Bouzebda: LMAC (Laboratory of Applied Mathematics of Compiègne), Université de Technologie de Compiègne, CS 60 319-60 203 Compiègne Cedex, 60203 Compiègne, France
Ali Laksaci: Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 62529, Saudi Arabia

Mathematics, 2025, vol. 13, issue 5, 1-39

Abstract: 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.

Keywords: kernel regression estimation; weak dependence data; quasi-associated variables; single functional index model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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