Abstract: BIC weighting is frequently applied to high-dimensional linear regressions when model averaging is used to address model selection uncertainty. It also plays a central role in model selection diagnostics. However, little research has been done on its consistency or weak consistency, which are crucial properties of model averaging methods. In addition, previous works on model averaging consistency do not consider categorical covariates. As such, with both continuous covariates and categorical predictors (with possibly diverging numbers of levels) allowed, we establish both the consistency and the weak consistency of BIC weighting.

Key words and phrases: BIC-p weighting, categorical predictors, consistency, weak consistency.