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

Censored quantile regression processes under dependence and penalization