Context tree selection: A unifying view
Context 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) .
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|
|Order Information:|| Postal: http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:121:y:2011:i:11:p:2488-2506. See general information about how to correct material in RePEc.
If references are entirely missing, you can add them using this form.