Robust model selection in generalized linear models

In this paper, we extend to generalized linear models the robust model selection methodology of Müller and Welsh (2005 As in Müller and Welsh (2005), we combine a robust penalized measure of fit to the sample with a robust measure of out of sample predictive ability that is estimated using a post-stratified m-out-of-n bootstrap. The method can be used to compare different estimators (robust and nonrobust) as well as different models. Specialized to linear models, the present methodology improves on Müller and Welsh (2005): we use a new bias-adjusted bootstrap estimator which avoids the need to include an intercept in every model and we establish an essential monotonicity condition more generally.