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

Abstract

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 coUinearity 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.

Keywords:

• Montecarlo simulation
• ridge regression
• breakdown point
• efficiency
• bounded influence