Robust Statistics, 2nd Edition

5Linear Regression 2

5.1 Introduction

Chapter 4 concentrated on robust regression estimators for situations where the predictor matrix contains no rows with high leverage, and only the responses may contain outliers. In that case a monotone M‐estimator is a reliable starting point for computing a robust scale estimator and a redescending M‐estimator. But when is random, outliers in operate as leverage points, and may completely distort the value of a monotone M‐estimator when some pairs are atypical. This chapter will deal with the case of random predictors and one of its focuses is on how to obtain good initial values for redescending M‐estimators.

The following example shows the failure of a monotone M‐estimator when is random and there is a single atypical observation.

Example 5.1 ...