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Consistency of the BIC order estimator
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## Consistency of the BIC order estimator

### Imre Csiszár and Paul C. Shields

**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.

*Copyright 1999 American Mathematical Society*

**Retrieve entire article **

#### Article Info

- ERA Amer. Math. Soc.
**05** (1999), pp. 123-127
- Publisher Identifier: S 1079-6762(99)00070-0
- 1991
*Mathematics Subject Classification*. Primary 62F12, 62M05; Secondary 62F13, 60J10
*Key words and phrases*. Bayesian information criterion, order estimation, ratio-typicality, Markov chains
- Received by the editors February 25, 1999
- Posted on October 19, 1999
- Communicated by Yitzhak Katznelson
- Comments (When Available)

**Imre Csiszár**

A. Rényi Institute of Mathematics, Hungarian Academy of Sciences, POB 127, 1364 Budapest, Hungary

*E-mail address:* `csiszar@math-inst.hu`

**Paul C. Shields **

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

*E-mail address:* `paul.shields@utoledo.edu`

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

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