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October 2012 Asymptotic properties of the maximum likelihood estimation in misspecified hidden Markov models
Randal Douc, Eric Moulines
Ann. Statist. 40(5): 2697-2732 (October 2012). DOI: 10.1214/12-AOS1047

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.

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Randal Douc. Eric Moulines. "Asymptotic properties of the maximum likelihood estimation in misspecified hidden Markov models." Ann. Statist. 40 (5) 2697 - 2732, October 2012. https://doi.org/10.1214/12-AOS1047

Information

Published: October 2012
First available in Project Euclid: 4 February 2013

zbMATH: 1373.62436
MathSciNet: MR3097617
Digital Object Identifier: 10.1214/12-AOS1047

Subjects:
Primary: 62M09
Secondary: 62F12

Keywords: Hidden Markov models , maximum likelihood estimator , misspecified models , state space models , strong consistency

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.40 • No. 5 • October 2012
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