Title :
The consistency of the BIC Markov order estimator
Author :
Csiszar, Imre ; Shields, Paul C.
Author_Institution :
Inst. of Math., Hungarian Acad. of Sci., Budapest, Hungary
Abstract :
We show that the BIC (Bayesian information criterion) estimator of the order of a Markov chain (with finite alphabet) gives the correct order, eventually almost surely as the sample size goes to ∞, thereby strengthening earlier consistency results that assumed an apriori bound on the order. A key tool is a strong typicality result for Markov sample paths. We also show that the Bayesian or MDL estimator, of which the BIC estimator is regarded as an approximation, fails to be consistent for the uniformly distributed i.i.d. process
Keywords :
Bayes methods; Markov processes; estimation theory; information theory; BIC Markov order estimator; Bayesian information criterion; MDL estimator; Markov chain; Markov sample paths; consistency; independent identically distributed process; uniformly distributed i.i.d. process; Bayesian methods; Estimation theory; Mathematics; Statistics;
Conference_Titel :
Information Theory, 2000. Proceedings. IEEE International Symposium on
Conference_Location :
Sorrento
Print_ISBN :
0-7803-5857-0
DOI :
10.1109/ISIT.2000.866316