Geodesic
Consistency of the BIC order estimator
Csiszár, Imre1 ; Shields, Paul2
1 A. Rényi Institute of Mathematics, Hungarian Academy of Sciences, POB 127, 1364 Budapest, Hungary
2 Mathematics Department, The University of Toledo, Toledo, OH 43606
Electronic research announcements of the American Mathematical Society, Tome 05 (1999), pp. 123-127.

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S1079-6762-99-00070-0

Csiszár, Imre 1 ; Shields, Paul 2

1 A. Rényi Institute of Mathematics, Hungarian Academy of Sciences, POB 127, 1364 Budapest, Hungary
2 Mathematics Department, The University of Toledo, Toledo, OH 43606 
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Csiszár, Imre; Shields, Paul. Consistency of the BIC order estimator. Electronic research announcements of the American Mathematical Society, Tome 05 (1999), pp. 123-127. doi : 10.1090/S1079-6762-99-00070-0. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-99-00070-0/

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