Consistency of the Bic Order Estimator
نویسندگان
چکیده
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.
منابع مشابه
The consistency of the BIC Markov order estimator
The Bayesian Information Criterion (BIC) estimates the order of a Markov chain (with nite alphabet A) from observation of a sample path x 1 ; x 2 ; : : :; x n , as that value k = ^ k that minimizes the sum of the negative logarithm of the k-th order maximum likelihood and the penalty term jAj k (jAj?1) 2 log n: We show that ^ k equals the correct order of the chain, eventually almost surely as ...
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