Asymptotic properties of the maximum likelihood estimation in misspecified hidden Markov models

Randal Douc (1, 2, 3) , Éric Moulines (4, 5)

1 TSP - CITI - Communications, Images et Traitement de l'Information
2 SAMOVAR - Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux
3 CNRS - Centre National de la Recherche Scientifique
4 LTCI - Laboratoire Traitement et Communication de l'Information
5 TSI - Département Traitement du Signal et des Images

Let (Y_k) be a stationary sequence on a probability space taking values in a standard Borel space Y. Consider the associated maximum likelihood estimator with respect to a parametrized family of hidden Markov models such that the law of the observations (Y_k) is not assumed to be described by any of the hidden Markov models of this family. In this paper we investigate the consistency of this estimator in such misspecified models under mild assumptions.

Mots clés: Strong consistency; Hidden Markov models; Maximum likelihood estimator; Misspecified models; State space models

Domaines: Traitement du signal et de l'image [eess.SP]

Randal Douc, Éric Moulines. Asymptotic properties of the maximum likelihood estimation in misspecified hidden Markov models. Annals of Statistics, 2012, 40 (5), pp.2697-2732. ⟨10.1214/12-AOS1047⟩. ⟨hal-00832818⟩