Consistency of the maximum likelihood estimator for general hidden Markov models
(2011) In Annals of Statistics 39(1). p.474-513- Abstract
- 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. 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... (More)
- 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. 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1868749
- author
- Douc, Randal ; Moulines, Eric ; Olsson, Jimmy LU and van Handel, Ramon
- organization
- publishing date
- 2011
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Hidden Markov models, maximum likelihood estimation, strong, consistency, V-uniform ergodicity, concentration inequalities, state, space models
- in
- Annals of Statistics
- volume
- 39
- issue
- 1
- pages
- 474 - 513
- publisher
- Institute of Mathematical Statistics
- external identifiers
-
- wos:000288183800016
- ISSN
- 0090-5364
- DOI
- 10.1214/10-AOS834
- language
- English
- LU publication?
- yes
- id
- a3f8d624-ac24-4b20-9d0b-981f37756a5c (old id 1868749)
- date added to LUP
- 2016-04-01 12:53:35
- date last changed
- 2018-11-21 20:10:01
@article{a3f8d624-ac24-4b20-9d0b-981f37756a5c,
abstract = {{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. 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.}},
author = {{Douc, Randal and Moulines, Eric and Olsson, Jimmy and van Handel, Ramon}},
issn = {{0090-5364}},
keywords = {{Hidden Markov models; maximum likelihood estimation; strong; consistency; V-uniform ergodicity; concentration inequalities; state; space models}},
language = {{eng}},
number = {{1}},
pages = {{474--513}},
publisher = {{Institute of Mathematical Statistics}},
series = {{Annals of Statistics}},
title = {{Consistency of the maximum likelihood estimator for general hidden Markov models}},
url = {{http://dx.doi.org/10.1214/10-AOS834}},
doi = {{10.1214/10-AOS834}},
volume = {{39}},
year = {{2011}},
}