Consistency of the Bayesian Information Criterion for a class of mixture autoregressive models

Applied statistics and neural networks communities are widely using Bayesian information criterion (BIC) for model selection tasks, although its convergence properties are not always theoretically established. This talk will be focused on showing the consistency of the BIC criterion for a wide class of mixture autoregressive models including mixtures of AR(p) models and multilayer perceptrons.The consistency of the BIC criterion is proved under some hypothesis involving essentially the bracketing entropy of the class of generalized score functions and is based on a uniform functional Central Limit Theorem for absolutely regular processes. The hypothesis of the main result are checked in the case of mixtures of AR(p) models and multilayer perceptrons with Gaussian noise. Numerical examples on both simulated and real-life data are presented to illustrate the result