Asymptotic properties of a conditional quantile estimator with randomly truncated data

Let Y be a response variable that is subject to left-truncation by a variable T . We consider the problem of estimating its conditional quantile function given a vector of covariates X . We derive almost sure (a.s.) consistency and asymptotic normality results for a kernel estimate of the conditional quantile function. Simulations are drawn to illustrate the results for finite samples.