Least squares type estimation of the transition density of a particular hidden Markov chain

Abstract : In this paper, we study the following model of hidden Markov chain: $Y_i=X_i+\varepsilon_i$, $ i=1,\dots,n+1$ with $(X_i)$ a real-valued stationary Markov chain and $(\varepsilon_i)_{1\leq i\leq n+1}$ a noise having a known distribution and independent of the sequence $(X_i)$. We present an adaptive estimator of the transition density obtained by minimization of an original contrast taking advantage of the regressive aspect of the problem. It is selected among a collection of projection estimators with a model selection method. The $L^2$-risk and its rate of convergence are evaluated for ordinary smooth noise and some simulations illustrate the method. Our estimator allows to avoid the drawbacks of the quotient estimators.
Type de document :
Article dans une revue
Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2008, 2, pp.1-39
Liste complète des métadonnées


https://hal.archives-ouvertes.fr/hal-00180219
Contributeur : Claire Lacour <>
Soumis le : jeudi 18 octobre 2007 - 11:41:23
Dernière modification le : mardi 11 octobre 2016 - 14:22:09
Document(s) archivé(s) le : dimanche 11 avril 2010 - 22:09:40

Fichier

prepubli.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00180219, version 1

Collections

Citation

Claire Lacour. Least squares type estimation of the transition density of a particular hidden Markov chain. Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2008, 2, pp.1-39. <hal-00180219>

Partager

Métriques

Consultations de
la notice

259

Téléchargements du document

129