The Annals of Statistics
- Ann. Statist.
- Volume 40, Number 5 (2012), 2697-2732.
Asymptotic properties of the maximum likelihood estimation in misspecified hidden Markov models
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Abstract
Let $(Y_{k})_{k\in\mathbb{Z}}$ be a stationary sequence on a probability space $(\Omega,\mathcal{A},\mathbb{P})$ taking values in a standard Borel space $\mathsf{Y}$. Consider the associated maximum likelihood estimator with respect to a parametrized family of hidden Markov models such that the law of the observations $(Y_{k})_{k\in\mathbb{Z}}$ 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.
Article information
Source
Ann. Statist. Volume 40, Number 5 (2012), 2697-2732.
Dates
First available in Project Euclid: 4 February 2013
Permanent link to this document
http://projecteuclid.org/euclid.aos/1359987535
Digital Object Identifier
doi:10.1214/12-AOS1047
Mathematical Reviews number (MathSciNet)
MR3097617
Zentralblatt MATH identifier
06344390
Subjects
Primary: 62M09: Non-Markovian processes: estimation
Secondary: 62F12: Asymptotic properties of estimators
Keywords
Strong consistency hidden Markov models maximum likelihood estimator misspecified models state space models
Citation
Douc, Randal; Moulines, Eric. Asymptotic properties of the maximum likelihood estimation in misspecified hidden Markov models. Ann. Statist. 40 (2012), no. 5, 2697--2732. doi:10.1214/12-AOS1047. http://projecteuclid.org/euclid.aos/1359987535.
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