On the rate of convergence of penalized likelihood context tree estimators
Florencia Leonardi · 2007
Abstract. We find upper bounds for the probability of error of the penalized-likelihood type context tree estimators, where the trees are not assumed to be finite. This estimators includes the well-known Bayesian Information Criterion (BIC). We show that the maximal decay for the probability of error can be achieved with a penalized term of the form n α, with 0 < α < 1. 1.