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.
 Publication:

arXiv eprints
 Pub Date:
 October 2011
 arXiv:
 arXiv:1110.0356
 Bibcode:
 2011arXiv1110.0356D
 Keywords:

 Mathematics  Statistics Theory
 EPrint:
 Published in at http://dx.doi.org/10.1214/12AOS1047 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)