Consider a parametrized family of general hidden Markov models, where both the observed and unobserved components take values in a complete separable metric space. We prove that the maximum likelihood estimator (MLE) of the parameter is strongly consistent under a rather minimal set of assumptions. As special cases of our main result, we obtain consistency in a large class of nonlinear state space models, as well as general results on linear Gaussian state space models and finite state models.
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A novel aspect of our approach is an information-theoretic technique for proving identifiability, which does not require an explicit representation for the relative entropy rate. Our method of proof could therefore form a foundation for the investigation of MLE consistency in more general dependent and non-Markovian time series. Also of independent interest is a general concentration inequality for V-uniformly ergodic Markov chains.
Publié le : 2011-02-15
Classification:
Hidden Markov models,
maximum likelihood estimation,
strong consistency,
V-uniform ergodicity,
concentration inequalities,
state space models,
60F10,
62B10,
62F12,
62M09,
60J05,
62M05,
62M10,
94A17
@article{1297779854,
author = {Douc, Randal and Moulines, Eric and Olsson, Jimmy and van Handel, Ramon},
title = {Consistency of the maximum likelihood estimator for general hidden Markov models},
journal = {Ann. Statist.},
volume = {39},
number = {1},
year = {2011},
pages = { 474-513},
language = {en},
url = {http://dml.mathdoc.fr/item/1297779854}
}
Douc, Randal; Moulines, Eric; Olsson, Jimmy; van Handel, Ramon. Consistency of the maximum likelihood estimator for general hidden Markov models. Ann. Statist., Tome 39 (2011) no. 1, pp. 474-513. http://gdmltest.u-ga.fr/item/1297779854/