Robust Regression When the True R2 is Mediocre

It is well known that several high-breakdown procedures can produce robust estimates of linear-regression coefficients despite substantial contamination in the data. In practice, however, the estimators’ robustness tends to be affected by the value of R2 in the uncontaminated part of the sample: when R2 is mediocre, commonly-recommended high-breakdown estimators may retain a substantial bias due to the contaminated data. This paper reports several simulations of simple and multiple regression where vertical outliers and bad-leverage observations affect 25% of the data and R2 is mediocre. One high-breakdown estimator appears to have small bias, very good coverage of a nominal 90% confidence interval, and precision that improves when the sample size is increased. The simulations are supplemented by applications to four real data sets