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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 -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

Email:
csiszar@math-inst.hu

**Paul C. Shields**

Affiliation:
Mathematics Department, The University of Toledo, Toledo, OH 43606

Email:
paul.shields@utoledo.edu

DOI:
https://doi.org/10.1090/S1079-6762-99-00070-0

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