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

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.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00693110
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Submitted on : Tuesday, May 1, 2012 - 8:19:21 PM
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Pierre Vandekerkhove. Consistent and asymptotically normal parameter estimates for hidden Markov mixtures of Markov models. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2005, 11 (1), pp.103--129. ⟨10.3150/bj/1110228244⟩. ⟨hal-00693110⟩

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