## The Annals of Statistics

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

#### 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

https://projecteuclid.org/euclid.aos/1359987535

Digital Object Identifier
doi:10.1214/12-AOS1047

Mathematical Reviews number (MathSciNet)
MR3097617

Zentralblatt MATH identifier
1373.62436

Subjects
Primary: 62M09: Non-Markovian processes: estimation
Secondary: 62F12: Asymptotic properties of estimators

#### 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. https://projecteuclid.org/euclid.aos/1359987535

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