A Robust Version of Mallows's <i>C</i> _P

Abstract

Abstract We present a robust version of Mallows's C P for regression models. It is defined by RC P = W Pσ2 - (U P - V P), where W P = ω i ω2 i r 2 i is a weighted residual sum of squares computed from a robust fit of model P, σ2 is a robust and consistent estimator of σ2 in the full model, and U P and V P are constants depending on the weight function and the number of parameters in model P. Good subset models are those with RC P close to V P or smaller than V P. When the weights are identically 1, W P becomes the residual sum of squares of a least squares fit, and RC P reduces to Mallows's C P. The robust model selection procedure based on RC P allows us to choose the models that fit the majority of the data by taking into account the presence of outliers and possible departures from the normality assumption on the error distribution. Together with the classical C P, the robust version suggests several models from which we can choose.