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Article Dans Une Revue Annals of Statistics Année : 2011

Consistency of the maximum likelihood estimator for general hidden Markov models

Résumé

Consider a parametrized family of general hidden Markov models, where both the observed and unobserved components take values in a complete separable metric space. We prove that the maximum likelihood estimator (MLE) of the parameter is strongly consistent under a rather minimal set of assumptions. As special cases of our main result, we obtain consistency in a large class of nonlinear state space models, as well as general results on linear Gaussian state space models and finite state models. A novel aspect of our approach is an information-theoretic technique for proving identifiability, which does not require an explicit representation for the relative entropy rate. Our method of proof could therefore form a foundation for the investigation of MLE consistency in more general dependent and non-Markovian time series. Also of independent interest is a general concentration inequality for V-uniformly ergodic Markov chains.

Dates et versions

hal-00633451 , version 1 (18-10-2011)

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Citer

Randal Douc, Éric Moulines, Jimmy Olsson, Ramon van Handel. Consistency of the maximum likelihood estimator for general hidden Markov models. Annals of Statistics, 2011, 39 (1), pp.474-513. ⟨10.1214/10-AOS834⟩. ⟨hal-00633451⟩
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