Consistency of the unlimited BIC Context Tree Estimator
Motivated by the Minimum Description Length principle , the BIC criterion has encountered a certain interest in the last years on model selection issues. In a recent article, Imre Csiszar and Zsolt Talata consider the case of Context Tree sources, a flexible generalization of Markov models widely used in data processing. They prove in particular that the BIC Context Tree estimator is consistent when its size is bounded a priori as o(\log n). We show here that this limitation is not necessary for finite context sources, and provide an algorithm to compute it efficiently.