| Texto completo | |
| Autor(es): |
Número total de Autores: 2
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| Afiliação do(s) autor(es): | [1] Telecom ParisTech, LTCI, CNRS, F-75634 Paris 13 - France
[2] Univ Sao Paulo, Inst Matemat & Estat, BR-05508 Sao Paulo - Brazil
Número total de Afiliações: 2
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| Tipo de documento: | Artigo Científico |
| Fonte: | Stochastic Processes and their Applications; v. 121, n. 11, p. 2488-2506, NOV 2011. |
| Citações Web of Science: | 9 |
| Resumo | |
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) | |
| Processo FAPESP: | 09/09411-8 - Estimação consistente de processos estocásticos com memória de comprimento variável: aplicações na modelagem de sequências biológicas |
| Beneficiário: | Florencia Graciela Leonardi |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |