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.
Publié le : 2010-07-15
Classification:
Context tree,
penalized maximum likelihood estimation,
Bayesian information criterion,
rate of convergence
@article{1271770274,
author = {Leonardi, Florencia},
title = {Some upper bounds for the rate of convergence of penalized likelihood context tree estimators},
journal = {Braz. J. Probab. Stat.},
volume = {24},
number = {1},
year = {2010},
pages = { 321-336},
language = {en},
url = {http://dml.mathdoc.fr/item/1271770274}
}
Leonardi, Florencia. Some upper bounds for the rate of convergence of penalized likelihood context tree estimators. Braz. J. Probab. Stat., Tome 24 (2010) no. 1, pp. 321-336. http://gdmltest.u-ga.fr/item/1271770274/