A biased-robust regression technique for the combined outlier-multicollinearity problem

The combined outlier-multicollinearity problem occurs frequently in regression data. Methods that successfully address this problem effectively combine biased and robust estimation techniques. A biased-robust estimator is proposed that uses a multi-stage generalized M-estimator with fully iterated ridge regression to successfully control both influence and collinearity in regression datasets. Two previously published approaches are compared with the proposal via simulation experiments. The best performing published technique is also compared with our proposal using a dataset containing a cloud of outliers and severe multicollinearity. The proposed biased-robust method outperforms the published technique both in simulation and the example.