Asymptotic behaviour of the MLE in hidden Markov models

François Le Gland 1 Laurent Mevel 1
1 SIGMA2 - Signal, models, algorithms
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, INRIA Rennes
Abstract : We consider an hidden Markov model (HMM) with multidimensional observations, and where the coe fficients (transition probability matrix, and observation conditional densities) depend on some unknown parameter. We investigate the asymptotic behaviour of the maximum likelihood estimator (MLE), as the number of observations increases to in nity. We exhibit the associated Kullback-Leibler information, we show that the MLE is consistent, i.e. converges to the set of minima of the Kullback-Leibler information. Finally, we prove that the MLE is asymptotically normal, under standard assumptions.
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Communication dans un congrès
Proceedings of the 4th European Control Conference, Bruxelles 1997, Jul 1997, Brussels, Belgium. 1997
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https://hal.inria.fr/hal-00912075
Contributeur : Francois Le Gland <>
Soumis le : vendredi 20 décembre 2013 - 18:13:56
Dernière modification le : mercredi 16 mai 2018 - 11:23:05

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  • HAL Id : hal-00912075, version 1

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François Le Gland, Laurent Mevel. Asymptotic behaviour of the MLE in hidden Markov models. Proceedings of the 4th European Control Conference, Bruxelles 1997, Jul 1997, Brussels, Belgium. 1997. 〈hal-00912075〉

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