  In this paper, we propose a class of high breakdown point estimators for the
linear regression model when the response variable contains censored
observations. These estimators are robust against high-leverage outliers and
they generalize the LMS (least median of squares), S, MM and $\tau$-estimators
for linear regression. An important contribution of this paper is that we can
define consistent estimators using a bounded loss function (or equivalently, a
redescending score function). Since the calculation of these estimators can be
computationally costly, we propose an efficient algorithm to compute them. We
illustrate their use on an example and present simulation studies that show
that these estimators also have good finite sample properties.
