Asymptotic normality of the maximum-likelihood estimator for general hidden Markov models

Hidden Markov models (HMMs) have during the last decade become a widespread tool for modeling sequences of dependent random variables. Inference for s uch models is usually based on the maximum-likelihood estimator (MLE), and consistency of the MLE for general HMMs was recently proved by Leroux. In t his paper me show that under mild conditions the MLE is also asymptotically normal and prove that the observed information matrix is a consistent esti mator of the Fisher information.