Consistency of the maximum likelihood estimator in hidden Markov models with trends - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2021

Consistency of the maximum likelihood estimator in hidden Markov models with trends

Luc Lehéricy
Augustin Touron

Résumé

A hidden Markov model with trends is a hidden Markov model whose emission distributions are translated by a trend that depends on the current hidden state and on the current time. Contrary to standard hidden Markov models, such processes are not homogeneous and cannot be made homogeneous by a simple de-trending step. We show that when the trends are polynomial, the maximum likelihood estimator is able to recover the trends together with the other parameters and is strongly consistent. More precisely, the supremum norm of the difference between the true trends and the estimated ones tends to zero. Numerical properties of the maximum likelihood estimator are assessed by a simulation study.
Fichier principal
Vignette du fichier
Trends.pdf (2.01 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03140231 , version 1 (15-12-2021)

Identifiants

Citer

Luc Lehéricy, Augustin Touron. Consistency of the maximum likelihood estimator in hidden Markov models with trends. 2021. ⟨hal-03140231⟩
15 Consultations
9 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More