Strong uniform consistency of a kernel conditional quantile estimator for censored and associated data

Abstract

In survival or reliability studies, it is common to deal with data which are not only incomplete but weakly dependent too. Random right-censoring and random left-truncation are two common forms of such data when they are neither independent nor strongly mixing but rather associated. In this paper, we focus on kernel estimation of the conditional quantile function of a strictly stationary associated random variable $T$ given a $d$-dimensional vector of covariates $X$, under random right-censoring. As main results, we establish a strong uniform consistency rate for the estimator. Then the finite sample performance of the estimator is illustrated on a simulation study.