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The optimal error exponent for Markov order estimation

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3 Author(s)
L. Finesso ; LADSEB, CNR, Padova, Italy ; Chuang-Chun Liu ; P. Narayan

We consider the problem of estimating the order of a stationary ergodic Markov chain. Our focus is on estimators which satisfy a generalized Neyman-Pearson criterion of optimality. Specifically, the optimal estimator minimizes the probability of underestimation among all estimators with probability of overestimation not exceeding a given value. Our main result identifies the best exponent of asymptotically exponential decay of the probability of underestimation. We further construct a consistent estimator, based on Kullback-Leibler divergences, which achieves the best exponent. We also present a consistent estimator involving a recursively computable statistic based on appropriate mixture distributions; this estimator also achieves the best exponent for underestimation probability

Published in:

IEEE Transactions on Information Theory  (Volume:42 ,  Issue: 5 )