Title :
Limit Theorems in Hidden Markov Models
Author_Institution :
Univ. of Hong Kong, Hong Kong, China
Abstract :
In this paper, under mild assumptions, we derive a law of large numbers, a central limit theorem with an error estimate, an almost sure invariance principle, and a variant of the Chernoff bound in finite-state hidden Markov models. These limit theorems are of interest in certain areas of information theory and statistics. Particularly, we apply the limit theorems to derive the rate of convergence of the maximum likelihood estimator in finite-state hidden Markov models.
Keywords :
entropy; hidden Markov models; maximum likelihood estimation; Chernoff bound; central limit theorem; entropy; error estimate; finite-state hidden Markov models; information theory; maximum likelihood estimator; Context; Convergence; Hidden Markov models; Information theory; Maximum likelihood estimation; Probabilistic logic; Random variables; Entropy; Shannon-McMillan-Breiman theorem; hidden Markov models; limit theorem;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2012.2226701
