An alternate version of the conceptual predictive statistic based on a symmetrized discrepancy measure

The conceptual predictive statistic, Cp, is a widely used criterion for model selection in linear regression. Cp serves as an estimator of a discrepancy, a measure that reflects the disparity between the generating model and a fitted candidate model. This discrepancy, based on scaled squared error loss, is asymmetric: an alternate measure is obtained by reversing the roles of the two models in the definition of the measure. We propose a variant of the Cp statistic based on estimating a symmetrized version of the discrepancy targeted by Cp. We claim that the resulting criterion provides better protection against overfitting than Cp, since the symmetric discrepancy is more sensitive towards detecting overspecification than its asymmetric counterpart. We illustrate our claim by presenting simulation results. Finally, we demonstrate the practical utility of the new criterion by discussing a modeling application based on data collected in a cardiac rehabilitation program at University of Iowa Hospitals and Clinics.