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High breakdown point robust regression with censored data. (English) Zbl 1132.62016

Summary: 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.

MSC:

62F35 Robustness and adaptive procedures (parametric inference)
62J05 Linear regression; mixed models
62H12 Estimation in multivariate analysis
65C60 Computational problems in statistics (MSC2010)
65C05 Monte Carlo methods
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