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Conference papers

Recursive identification 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 a hidden Markov model (HMM) with multidimensional observations, and where the coefficients (transition probability matrix, and observation conditional densities) depend on some unknown parameter. We study the asymptotic behaviour of two recursive estimators, the recursive maximum likelihood estimator (RMLE), and the recursive conditional least squares estimator (RCLSE), as the number of observations increases to infinity. Firstly, we exhibit the contrast functions associated with the two non-recursive estimators, and we prove that the recursive estimators converge a.s. to the set of stationary points of the corresponding contrast function. Secondly, we prove that the two recursive estimators are asymptotically normal
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François Le Gland, Laurent Mevel. Recursive identification in hidden Markov models. Proceedings of the 36th Conference on Decision and Control, San Diego 1997, IEEE--CSS, Dec 1997, San Diego, United States. pp.3468-3473, ⟨10.1109/CDC.1997.652384⟩. ⟨hal-00912077⟩



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