  In this paper, we extend to generalized linear models (including logistic and
other binary regression models, Poisson regression and gamma regression models)
the robust model selection methodology developed by Mueller and Welsh (2005;
JASA) for linear regression models. As in Mueller and Welsh (2005), we combine
a robust penalized measure of fit to the sample with a robust measure of out of
sample predictive ability which is estimated using a post-stratified m-out-of-n
bootstrap. A key idea is that the method can be used to compare different
estimators (robust and nonrobust) as well as different models. Even when
specialized back to linear regression models, the methodology presented in this
paper improves on that of Mueller and Welsh (2005). In particular, we use a new
bias-adjusted bootstrap estimator which avoids the need to centre the
explanatory variables and to include an intercept in every model. We also use
more sophisticated arguments than Mueller and Welsh (2005) to establish an
essential monotonicity condition.
