The Annals of Statistics

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

Peter J. Bickel, Ya’acov Ritov, and Tobias Rydén

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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 Leroux. In this paper 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.

Article information

Ann. Statist., Volume 26, Number 4 (1998), 1614-1635.

First available in Project Euclid: 21 June 2002

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Zentralblatt MATH identifier

Primary: 62M09

Hidden Markov model incomplete data missing data, asymptotic normality


Bickel, Peter J.; Ritov, Ya’acov; Rydén, Tobias. Asymptotic normality of the maximum-likelihood estimator for general hidden Markov models. Ann. Statist. 26 (1998), no. 4, 1614--1635. doi:10.1214/aos/1024691255.

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