  We consider the problem of nonparametric quantile regression for twice
censored data. Two new estimates are presented, which are constructed by
applying concepts of monotone rearrangements to estimates of the conditional
distribution function. The proposed methods avoid the problem of crossing
quantile curves. Weak uniform consistency and weak convergence is established
for both estimates and their finite sample properties are investigated by means
of a simulation study. As a by-product, we obtain a new result regarding the
weak convergence of the Beran estimator for right censored data on the maximal
possible domain, which is of its own interest.
