Wilcoxon-type generalized Bayesian information criterion

We extend the basic idea of Schwarz (1978) and develop a generalized Bayesian information criterion for regression model selection. The new criterion relaxes the usually strong distributional assumption associated with Schwarz’s BIC by adopting a Wilcoxon-type dispersion function and appropriately adjusting the penalty term. We establish that the Wilcoxon-type generalized BIC preserves the consistency property of Schwarz’s BIC without its need to assume a parametric likelihood. We also show that it outperforms Schwarz’s BIC with heavier-tailed data in the sense that asymptotically it can yield substantially smaller L2 risk. On the other hand, when the data are normally distributed, both criteria have similar L2 risk. The new criterion function is convex and can be conveniently computed via existing statistical software.