Fast and robust model selection criterion in generalized linear models

Selecting the optimal model from a set of competing models is an essential task in statistics. The focus is on selecting the best subset of available explanatory variables in generalized linear models. It is well-known that standard model selection criteria for generalized linear models are extremely sensitive to contamination in the data. Therefore, robust alternatives are introduced. Particular attention is paid to robust model selection criteria based on resampling techniques. However, a recalculation of robust criteria for each resample is computer intensive because robust criteria are already computationally intensive compared to their non-robust versions. To reduce the computational burden, a modified resampling procedure, inspired by the fast and robust bootstrap method, is proposed. Moreover, it is shown that this modification still yields consistent model selection criterion, in the sense that the optimal model is selected with probability one as the sample size grows to infinity. The performance of the proposed methodology is evaluated empirically by a simulation study and illustrated on real data examples.status: publishe