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

High breakdown point robust regression with censored data