| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Telecom ParisTech, LTCI, CNRS, F-75634 Paris 13 - France
[2] Univ Sao Paulo, Inst Matemat & Estat, BR-05508 Sao Paulo - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | Stochastic Processes and their Applications; v. 121, n. 11, p. 2488-2506, NOV 2011. |
| Web of Science Citations: | 9 |
| Abstract | |
Context tree models have been introduced by Rissanen in {[}25] as a parsimonious generalization of Markov models. Since then, they have been widely used in applied probability and statistics. The present paper investigates non-asymptotic properties of two popular procedures of context tree estimation: Rissanen's algorithm Context and penalized maximum likelihood. First showing how they are related, we prove finite horizon bounds for the probability of over- and under-estimation. Concerning overestimation, no boundedness or loss-of-memory conditions are required: the proof relies on new deviation inequalities for empirical probabilities of independent interest. The under-estimation properties rely on classical hypotheses for processes of infinite memory. These results improve on and generalize the bounds obtained in Duarte et al. (2006) {[}12], Galves et al. (2008) {[}18], Galves and Leonardi (2008) {[}17], Leonardi (2010) {[}22], refining asymptotic results of Buhlmann and Wyner (1999) {[}4] and Csiszar and Talata (2006) {[}9]. (C) 2011 Elsevier B.V. All rights reserved. (AU) | |
| FAPESP's process: | 09/09411-8 - Consistent estimation of stochastic processes with variable length memory: applications to the modeling of biological sequences |
| Grantee: | Florencia Graciela Leonardi |
| Support Opportunities: | Regular Research Grants |