Wilcoxon-type generalized Bayesian information criterion

We 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 of Schwarz's BIC without the 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 L-sub-2 risk. On the other hand, when the data are normally distributed, both criteria have similar L-sub-2 risk. The new criterion function is convex and can be conveniently computed using existing statistical software. Our proposal provides a flexible yet highly efficient alternative to Schwarz's BIC; at the same time, it broadens the scope of Wilcoxon inference, which has played a fundamental role in classical nonparametric analysis. Copyright 2009, Oxford University Press.