We consider a lifetime data with covariates which are subject to the right censorship. In this context, it is interesting to study the conditional distribution function of the lifetime and the corresponding conditional quantile function. In this paper, we establish strong representation of the conditional quantile estimator when the data exhibit some of kind of independence. As a consequence of this representation, we establish the asymptotic normality of this conditional quantile estimator.

kernel estimator, conditional quantile, strong representation, asymptotic normality, right censoring.