Bernoulli

  • Bernoulli
  • Volume 7, Number 3 (2001), 381-420.

Asymptotics of the maximum likelihood estimator for general hidden Markov models

Randal Douc and Catherine Matias

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Abstract

In this paper, we consider the consistency and asymptotic normality of the maximum likelihood estimator for a possibly non-stationary hidden Markov model where the hidden state space is a separable and compact space not necessarily finite, and both the transition kernel of the hidden chain and the conditional distribution of the observations depend on a parameter θ. For identifiable models, consistency and asymptotic normality of the maximum likelihood estimator are shown to follow from exponential memorylessness properties of the state prediction filter and geometric ergodicity of suitably extended Markov chains.

Article information

Source
Bernoulli Volume 7, Number 3 (2001), 381-420.

Dates
First available in Project Euclid: 22 March 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1080004757

Mathematical Reviews number (MathSciNet)
MR2002e:62081

Zentralblatt MATH identifier
0987.62018

Keywords
asymptotic normality consistency geometric ergodicity hidden Markov models identifiability maximum likelihood estimation

Citation

Douc, Randal; Matias, Catherine. Asymptotics of the maximum likelihood estimator for general hidden Markov models. Bernoulli 7 (2001), no. 3, 381--420. https://projecteuclid.org/euclid.bj/1080004757.


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