Consistency of the maximum likelihood estimator for general hidden Markov models

Details Consistency of the maximum likelihood estimator for general hidden Markov models Consistency of the maximum likelihood estimator for general hidden Markov models

2009-12-22

arxiv.org/abs/0912.4480v2

Annals of Statistics 2011, Vol. 39, No. 1, 474-513

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/10-AOS834 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/10-AOS834

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.

Affiliated with

Also associated with

No associations

Rating

Consistency of the maximum likelihood estimator for general hidden Markov models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Consistency of the maximum likelihood estimator for general hidden Markov models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Consistency of the maximum likelihood estimator for general hidden Markov models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-307750