Non Parametric Regression Quantile Estimation for Dependent Functional Data under Random Censorship: Asymptotic Normality

In this paper we study a smooth estimator of the regression quantile function in the censorship model when the covariates take values in some abstract function space. The main goal of this paper is to establish the asymptotic normality of the kernel estimator of the regression quantile, under α-mixing condition and, on the concentration properties on small balls probability measure of the functional regressors. Some applications and particular cases are studied. This study can be applied in time series analysis to the prediction and building confidence bands. Some simulations are drawn to lend further support to our theoretical results and to compare the quality of behavior of the estimator for finite samples with different rates of censoring and sizes.