Context tree selection: A unifying view
AbstractContext tree models have been introduced by Rissanen in  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: Rissanenâs 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 over-estimation, 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 etÂ al. (2006) , Galves etÂ al. (2008) , Galves and Leonardi (2008) , Leonardi (2010) , refining asymptotic results of Böhlmann and Wyner (1999)  and Csiszár and Talata (2006) .
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by Elsevier in its journal Stochastic Processes and their Applications.
Volume (Year): 121 (2011)
Issue (Month): 11 (November)
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description
You can help add them by filling out this form.
reading list or among the top items on IDEAS.Access and download statisticsgeneral information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If references are entirely missing, you can add them using this form.