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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Abstract

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

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

Dates
First available in Project Euclid: 21 June 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1024691255

Digital Object Identifier
doi:10.1214/aos/1024691255

Mathematical Reviews number (MathSciNet)
MR1647705

Zentralblatt MATH identifier
0932.62097

Subjects
Primary: 62M09

Keywords
Hidden Markov model incomplete data missing data, asymptotic normality

Citation

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. https://projecteuclid.org/euclid.aos/1024691255


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