Asymptotic normality of the maximum-likelihood estimator for general hidden Markov models. (English) Zbl 0932.62097

Summary: Hidden Markov models (HMMs) have during the last decade become a widespread tool for modeling sequences of dependent random variables. Inference for such models is usually based on the maximum-likelihood estimator (MLE), and consistency of the MLE for general HMMs was recently proved by {B. G. Leroux} [Stochastic Processes Appl. 40, No. 1, 127-143 (1992; Zbl 0738.62081)]. We show that under mild conditions the MLE is also asymptotically normal and prove that the observed information matrix is a consistent estimator of the Fisher information.


62M05 Markov processes: estimation; hidden Markov models
62F12 Asymptotic properties of parametric estimators
62M09 Non-Markovian processes: estimation


Zbl 0738.62081
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