- Recherche et sélection de publications
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The maximizing set of the asymptotic normalized log-likelihood for partially observed Markov chains
- Randal Douc #1, François Roueff #2, Tepmony Sim #2
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| #1 |
Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux (SAMOVAR)
- CNRS : UMR5157
- Institut Mines-Télécom
- Télécom SudParis
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| #2 |
Laboratoire Traitement et Communication de l'Information [Paris] (LTCI)
- Télécom ParisTech
- CNRS : UMR5141
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- References
- Annals of Applied Probability, 2016, vol. 26, n° 4, pp. 2357-2383
- Abstract
This paper deals with a parametrized family of partially observed bivariate Markov chains. We establish that, under very mild assumptions, the limit of the normalized log-likelihood function is maximized when the parameters belong to the equivalence class of the true parameter, which is a key feature for obtaining the consistency of the maximum likelihood estimators (MLEs) in well-specified models. This result is obtained in the general framework of partially dom- inated models. We examine two specific cases of interest, namely, hidden Markov models (HMMs) and observation-driven time series models. In contrast with previous approaches, the identifiability is addressed by relying on the uniqueness of the invariant distribution of the Markov chain associated to the complete data, regardless its rate of convergence to the equilibrium.
- Keywords
- consistency, ergodicity, hidden Markov models, maximum likelihood, observation-driven models, time series of counts
- Category
- Article in peer reviewed Journal
- Research Area(s)
- Statistics
Mathematics
- Identifier(s)
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DOI 10.1214/15-AAP1149
HAL ref. hal-01080955
Bibliographic key doumonrou2016maximizing
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- Last update
- on september 02, 2016
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