Unrestricted BIC context tree estimation for not necessarily finite memory processes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
On rate of convergence of statistical estimation of stationary ergodic processes
IEEE Transactions on Information Theory
| Hi-index | 754.90 |
For Markov chains of arbitrary order, with finite alphabet A, almost sure sense limit theorems are proved on relative frequencies of k-blocks, and of symbols preceded by a given k-block, when k is permitted to grow as the sample size n grows. As-an application, the-consistency of two kinds of minimum description length (MDL) Markov order estimators is proved, with upper bound o(log n), respectively, α log n with α < 1/log |A|, on the permissible value of the estimated order. It was shown by Csiszar and Shields (see Ann. Statist., vol.28, p.1601-1619, 2000) that in the absence of any bound, or with bound α log n with large α consistency fails