On the robustness of Mallows’ C_p criterion

Abstract

This article proposes robust versions of Mallows’ C_p criterion to select the best variables for a multiple linear regression model with a small number of variables in the presence of outliers. The robustness measures of Mallows’ C_p were studied in more detail. Moreover, the breakdown point, influence function, and gross-error sensitivity were derived. The same formulation of classical C_p was used with a high breakdown estimator. The performance of the proposed robust C_p criteria based on M estimators and the classical non-robust C_p were compared via a simulation study. The results of the simulation study and application on real data showed that the proposed C_p successfully selected the appropriate model especially in the case of leverage points. These findings pave the way for the use of the proposed robust C_p criteria for model selection in the presence of multicellularity problem via least absolute shrinkage and selection operator model.

Keywords:

• Mallows’ Cp
• Robust estimators
• Robust Mallows’ Cp
• Robust variable selection

Acknowledgements

We are grateful to the editor and anonymous reviewers for their valuable comments on earlier draft of this paper.