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Markov chain order estimation based on the chi‐square divergence
Author(s) -
Baigorri Angel Rodolfo,
Gonçalves Cátia Regina,
Resende Paulo Angelo Alves
Publication year - 2014
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11225
Subject(s) - akaike information criterion , mathematics , bayesian information criterion , markov chain , estimator , statistics , information criteria , context (archaeology) , model selection , paleontology , biology
In the selection model context, several alternatives for estimating the order of a Markov chain have been proposed. The Akaike's information criterion, AIC, is the best known and most used alternative, in spite of its inconsistency. The Bayesian information criterion (BIC) and the efficient determination criterion (EDC) have been stated as strong consistent approaches. The success of the AIC is mainly a result of its better performance when compared with the widely known consistent alternatives. In this work, we define a few objects which capture relevant information from the sample of a finite Markov chain and we use the chi‐square divergence to define a new estimator for the Markov chain order, named GDL. Finally, we show numerical simulations and a simple application to compare the proposed alternative with AIC, BIC and EDC. The Canadian Journal of Statistics 42: 563–578; 2014 © 2014 Statistical Society of Canada