Some upper bounds for the rate of convergence of penalized likelihood context tree estimators
Abstract
Description
We find upper bounds for the probability of underestimation and overestimation errors in penalized likelihood context tree estimation. The bounds are explicit and applies to processes of not necessarily finite memory. We allow for general penalizing terms and we give conditions over the maximal depth of the estimated trees in order to get strongly consistent estimates. This generalizes previous results obtained in the case of estimation of the order of a Markov chain.
13 pages, some changes in the organization of the paper from previous version
13 pages, some changes in the organization of the paper from previous version