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- W1882386031 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 authorsâ article to appear in The Annals of Statistics." @default.
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- W1882386031 date "1999-10-19" @default.
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- W1882386031 title "Consistency of the BIC order estimator" @default.
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- W1882386031 doi "https://doi.org/10.1090/s1079-6762-99-00070-0" @default.
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