Asymptotic normality for a smooth kernel estimator of the conditional quantile for censored time series

In this paper we study a smooth estimator of the conditional quantile function in the censorship model, when the data exhibit some dependence structure. We show that, under some regularity conditions, the kernel estimator of the conditional quantile suitably normalised is asymptotically normally distributed. An application to prediction and confidence intervals is also given. Some simulations have been drawn to lend further support to our theoretical results of the normality for finite samples sizes.