Strong uniform consistency of a nonparametric estimator of a conditional quantile for censored dependent data and functional regressors

Let. (T, C, X) be a vector of random variables (rvs) where T, C and X are the interest variable, a right censoring rv and a covariate, respectively. In this paper, we study the kernel conditional quantile estimation in the dependent case and when the covariable takes values in an infinite-dimension space. An estimator of the conditional quantile is given and, under some regularity conditions, among which the small-ball probability for the covariate, its uniform strong convergence with rates is established.