Robust Regression

Robust regression is an alternative to ordinary least squares that can be appropriately used when there is evidence that the distribution of the error term is nonnormal, and/or there are outliers that affect the equation. This chapter contains a survey of robust regression techniques, with some methods covered in detail. The historical development of most of the different classes of robust regression estimators is traced by Rousseeuw and Leroy, who indicate that such estimators date from Edgeworth. The chapter provides a survey the different classes of robust regression estimators. It discusses most of the robust regression estimators that have been presented in the literature, starting with high breakdown point (HBP) estimators. Although least median of squares (LMS) estimator, least trimmed squares (LTS) estimator and S-estimators have generally been presented as standalone procedures, they can also be used in conjunction with a bounded influence estimator.