On model selection via stochastic complexity in robust linear regression

We study model selection for linear models when there are possible outliers both in the response and the predictor variables. We derive a new criterion based on generalized Huberization and on the newly developed theory of stochastic complexity. For purpose of comparison, several other criteria are also studied. Some asymptotic properties concerning strong consistency of selecting the optimal model by these criteria are given under general conditions. Other features like robustness against outliers and effect of signal-to-noise ratio are discussed as well. Finally, an example and a simulation study are presented to evaluate the finite sample performance.