Quantile regression with censored data using generalized L(1) minimization

We propose a way to estimate a parametric quantile function when the dependent variable, e.g. the survival time, is censored. We discuss one way to do this, transforming the problem of finding the p-quantile for the true, uncensored, survival times into a problem of finding the q-quantile for the observed, censored, times. The q-value involves the distribution of the censoring times, which is unknown. The estimation of the quantile function is done using the asymmetric L(1) technique with weights involving local Kaplan-Meier estimates of the distribution of the censoring limit.