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Consistency of the BIC order estimator

Authors: Imre Csiszár and Paul C. Shields
Journal: Electron. Res. Announc. Amer. Math. Soc. 5 (1999), 123-127
MSC (1991): Primary 62F12, 62M05; Secondary 62F13, 60J10
Published electronically: October 19, 1999
MathSciNet review: 1715427
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Abstract: We announce two results on the problem of estimating the order of a Markov chain from observation of a sample path. First is that the Bayesian Information Criterion (BIC) leads to an almost surely consistent estimator. Second is that the Bayesian minimum description length estimator, of which the BIC estimator is an approximation, fails to be consistent for the uniformly distributed i.i.d. process. A key tool is a strong ratio-typicality result for empirical $k$-block distributions. Complete proofs are given in the authors’ article to appear in The Annals of Statistics.

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Additional Information

Imre Csiszár
Affiliation: A. Rényi Institute of Mathematics, Hungarian Academy of Sciences, POB 127, 1364 Budapest, Hungary

Paul C. Shields
Affiliation: Mathematics Department, The University of Toledo, Toledo, OH 43606

Keywords: Bayesian information criterion, order estimation, ratio-typicality, Markov chains
Received by editor(s): February 25, 1999
Published electronically: October 19, 1999
Additional Notes: First author supported in part by a joint NSF-Hungarian Academy grant 92
Second author supported in part by a joint NSF-Hungarian Academy grant INT-9515485
Communicated by: Yitzhak Katznelson
Article copyright: © Copyright 1999 American Mathematical Society