ABSTRACT
This chapter summarizes several robust regression estimators that seem to be particularly useful, with the understanding that no single estimator is always optimal. It describes methods with heteroscedasticity in a relatively effective manner. The least median of squares (LMS) regression estimator was first proposed by Hampel and further developed by Rousseeuw. The projection outlier detection method appears to be a relatively good choice followed by the Theil-Sen estimator. The chapter proposes many regression estimators that can have substantial advantages over the ordinary least squares estimator. There are two general approaches to measuring the strength of an association in a robust manner. The first is to use a robust analog of Pearson's correlation that is not based on any particular regression estimator. The other approach first fits a regression line to the data, and then the strength of the association is measured based on this fit.
