Local linear estimation for the censored functional regression

Fatimah A Almulhim; Torkia Merouan; Mohammed B. Alamari; Boubaker Mechab; Fatimah A Almulhim; Torkia Merouan; Mohammed B. Alamari; Boubaker Mechab

doi:10.3934/math.2024679

AIMS Mathematics

2024, Volume 9, Issue 6: 13980-13997. doi: 10.3934/math.2024679

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Research article

Local linear estimation for the censored functional regression

1.
Department of Mathematical Sciences, College of Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2.
Laboratory of Statistics and Stochastic Processes, University of Djillali Liabes, BP 89, Sidi Bel Abbes 22000, Algeria
3.
Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia

Received: 18 February 2024 Revised: 21 March 2024 Accepted: 29 March 2024 Published: 16 April 2024
MSC : 62R20, 62G05, 62G08

This work considers the Local Linear Estimation (LLE) of the conditional functional mean. This regression model is used when the independent variable is functional, and the dependent one is a censored scalar variable. Under standard postulates, we establish the asymptotic distribution of the LLE by proving its asymptotic normality. The obtained results show the superiority of the LLE approach over the functional local constant one. The feasibility of the studied model is demonstrated using artificial data. Finally, the usefulness of the obtained asymptotic distribution in incomplete functional data is highlighted through a real data application.
- regression function,
- functional data,
- asymptotic normality,
- local linear estimation,
- Kaplan-Meier estimator
Citation: Fatimah A Almulhim, Torkia Merouan, Mohammed B. Alamari, Boubaker Mechab. Local linear estimation for the censored functional regression[J]. AIMS Mathematics, 2024, 9(6): 13980-13997. doi: 10.3934/math.2024679

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Abstract

This work considers the Local Linear Estimation (LLE) of the conditional functional mean. This regression model is used when the independent variable is functional, and the dependent one is a censored scalar variable. Under standard postulates, we establish the asymptotic distribution of the LLE by proving its asymptotic normality. The obtained results show the superiority of the LLE approach over the functional local constant one. The feasibility of the studied model is demonstrated using artificial data. Finally, the usefulness of the obtained asymptotic distribution in incomplete functional data is highlighted through a real data application.

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