Asymptotic normality of local linear functional regression estimator based upon censored data

This article is concerned with the local linear non parametric regression estimator of a right censored scalar response random variable, given a functional random covariate. First, we investigate its asymptotic normality under the concentration properties of small ball probability functions. Then, we apply the results to present the asymptotic (1−α) confidence interval of the regression function for 0<α<1. To lend further support to our theoretical results, we carry out a simulation study to illustrate the performance and the asymptotic Gaussian behavior of our estimator. Finally, an application to real data is provided.