High breakdown point robust regression with censored data

TL;DR

This paper introduces high breakdown point robust regression estimators for censored data, extending existing methods, with an efficient algorithm and demonstrated strong finite sample performance.

Contribution

It develops a new class of robust regression estimators for censored data that are computationally feasible and theoretically consistent.

Findings

Estimators are robust against high-leverage outliers.

Simulation studies show good finite sample properties.

The method generalizes several existing robust estimators.

Abstract

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.