Robust Measures of Evidence for Variable Selection

Abstract

We briefly give an overview of two general methods for submodel selection of an adopted parametric model, namely the Akaike Information Criterion and the Wald test procedure of Sommer and Huggins [204]. In the case of linear regression, we relate them to Mallows’ C _P and the robust version RC _P of Ronchetti and Staudte. Then we propose a new method for robustly finding acceptable submodels using weights of evidence for hypotheses regarding the noncentrality parameter of the Wald test statistic. The theory is illustrated with applications to linear and logistic regression, and to finding the order of time series.