# Consistency of the Maximum Likelihood Estimator for general hidden Markov models

Abstract : 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.
Keywords :
Type de document :
Pré-publication, Document de travail
2009
Domaine :
Liste complète des métadonnées

https://hal-imt.archives-ouvertes.fr/hal-00442774
Contributeur : Eric Moulines <>
Soumis le : mardi 22 décembre 2009 - 15:02:59
Dernière modification le : jeudi 11 janvier 2018 - 06:23:38
Document(s) archivé(s) le : vendredi 18 juin 2010 - 00:03:24

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### Identifiants

• HAL Id : hal-00442774, version 1
• ARXIV : 0912.4480

### Citation

Randal Douc, Eric Moulines, Jimmy Olsson, Ramon Van Handel. Consistency of the Maximum Likelihood Estimator for general hidden Markov models. 2009. 〈hal-00442774〉

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