  We consider quantile regression processes from censored data under dependent
data structures and derive a uniform Bahadur representation for those
processes. We also consider cases where the dimension of the parameter in the
quantile regression model is large. It is demonstrated that traditional
penalized estimators such as the adaptive lasso yield sub-optimal rates if the
coefficients of the quantile regression cross zero. New penalization techniques
are introduced which are able to deal with specific problems of censored data
and yield estimates with an optimal rate. In contrast to most of the
literature, the asymptotic analysis does not require the assumption of
independent observations, but is based on rather weak assumptions, which are
satisfied for many kinds of dependent data.
