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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