Title :
Convergence rates of the maximum likelihood estimator of hidden Markov models
Author :
Mevel, Laurent ; Finesso, Lorenzo
Author_Institution :
IRISA/INRIA, Rennes, France
Abstract :
We derive the almost sure rate of convergence of the maximum likelihood estimator of the parameters of a hidden Markov model with continuous observations and finite state space. The analysis is based on the geometric ergodicity properties of the prediction filter and its derivatives. As an example of application of these results we prove that, also in this context, the likelihood ratio is a consistent statistic for model selection
Keywords :
convergence; filtering theory; hidden Markov models; matrix algebra; maximum likelihood estimation; prediction theory; probability; almost sure convergence rate; continuous observations; finite state space; geometric ergodicity properties; likelihood ratio; model selection; prediction filter; Context modeling; Convergence; Filters; Hidden Markov models; Maximum likelihood estimation; Parameter estimation; Probability distribution; State estimation; State-space methods; Statistics;
Conference_Titel :
Decision and Control, 2000. Proceedings of the 39th IEEE Conference on
Conference_Location :
Sydney, NSW
Print_ISBN :
0-7803-6638-7
DOI :
10.1109/CDC.2001.914668
