On the Robustness of Mallows’ Cp Criterion

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