University of Toledo, Ohio
The problem addressed is the (almost-sure) consistent estimation of the order of a (finite state) Markov chain from observation a sample path, as path length goes to infinity. It is shown that the order that minimizes the usual penalized maximum likelihood estimate is consistent. This sharpens earlier results that assumed an apriori bound on the order. The method of proof uses a new result about the ratio of the empirical distribution of k-blocks to the true distribution in the case when k is allowed to grow with sample path length.
This is joint work with Imre Csiszar.