Title: High breakdown point robust regression with censored data

Matias Salibian-Barrera - Carleton University
Victor Yohai - University of Buenos Aires

In this talk we discuss robust regression estimates for censored data. The extension of the classical Least Squares estimates to the cases of censored responses was first proposed by Miller (1976) and Buckley and James (1979). More recently Ritov (1990) and Lai and Ying (1994) studied M-estimates for censored responses. Unfortunately, these estimates require a monotone estimating equation and hence are robust only to low-leverage outliers. We propose an extension of high-breakdown regression estimates to the case of censored response variables. In particular, our approach extends the classes of LMS estimates [Rousseeuw, 1984], S-estimates [Rousseeuw and Yohai, 1984], MM-estimates [Yohai, 1987], tau-estimates [Yohai and Zamar, 1988], P-estimates [Maronna and Yohai, 1993] and maximum depth estimates [Rousseeuw and Hubert, 1999]. Simulation studies show that these estimates have good finite sample properties. Examples and an algorithm to compute these estimators will also be discussed.