Asymptotical statistics of misspecified hidden Markov models

Author

Mevel, Laurent ; Finesso, Lorenzo

Author_Institution

IRISA/INRIA, France

Volume

49

Issue

7

fYear

2004

fDate

7/1/2004 12:00:00 AM

Firstpage

1123

Lastpage

1132

Abstract

This paper deals with the problem of modeling data generated by an ergodic stochastic process as the output of a hidden Markov model (HMM). More specifically, we consider the problem of fitting a parametric family of HMM with continuous output to an ergodic stochastic process with continuous values, which does not necessarily belong to the family. In this context, we derive the main asymptotic results: almost sure consistency of the maximum likelihood estimator, asymptotic normality of the estimation error and the exact rates of almost sure convergence.

Keywords

hidden Markov models; maximum likelihood estimation; Gaussian random variables; asymptotical statistics; data modeling; ergodic stochastic process; estimation error; maximum likelihood estimation; misspecified hidden Markov models; Approximation algorithms; Convergence; Estimation error; Filtering theory; Hidden Markov models; Maximum likelihood estimation; Parametric statistics; Random variables; Reduced order systems; Stochastic processes; Estimation; HMMs; filtering theory; hidden Markov models; identification; misspecification;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2004.831156

Filename

1310466