Bernoulli

  • Bernoulli
  • Volume 11, Number 1 (2005), 103-129.

Consistent and asymptotically normal parameter estimates for hidden Markov mixtures of Markov models

Pierre Vandekerkhove

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Abstract

We introduce a new missing-data model, based on a mixture of K Markov processes, and consider the general problem of identifying its parameters. We point out in detail the main difficulties of statistical inference for such models: complete likelihood calculation, parametrization of the stationary distribution and identifiability. We propose a general tractable approach for estimating these models (admitting parametrization of the stationary distribution and identifiability) and check in detail that our assumptions are fully satisfied for a Markov mixture of two linear AR(1) models with Gaussian noise. Finally, a Monte Carlo method is proposed to calculate the split data likelihood of this model when no analytic expression for the invariant probability densities of the Markov processes is known.

Article information

Source
Bernoulli, Volume 11, Number 1 (2005), 103-129.

Dates
First available in Project Euclid: 7 March 2005

Permanent link to this document
https://projecteuclid.org/euclid.bj/1110228244

Digital Object Identifier
doi:10.3150/bj/1110228244

Mathematical Reviews number (MathSciNet)
MR2121457

Zentralblatt MATH identifier
1060.62093

Keywords
hidden Markov chain incomplete data Markov chain mixture statistical inference

Citation

Vandekerkhove, Pierre. Consistent and asymptotically normal parameter estimates for hidden Markov mixtures of Markov models. Bernoulli 11 (2005), no. 1, 103--129. doi:10.3150/bj/1110228244. https://projecteuclid.org/euclid.bj/1110228244


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