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Parameter Estimation in Pair‐hidden Markov Models

Author

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  • ANA ARRIBAS‐GIL
  • ELISABETH GASSIAT
  • CATHERINE MATIAS

Abstract

. This paper deals with parameter estimation in pair‐hidden Markov models. We first provide a rigorous formalism for these models and discuss possible definitions of likelihoods. The model is biologically motivated and therefore naturally leads to restrictions on the parameter space. Existence of two different information divergence rates is established and a divergence property is shown under additional assumptions. This yields consistency for the parameter in parametrization schemes for which the divergence property holds. Simulations illustrate different cases which are not covered by our results.

Suggested Citation

  • Ana Arribas‐Gil & Elisabeth Gassiat & Catherine Matias, 2006. "Parameter Estimation in Pair‐hidden Markov Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 651-671, December.
    • Handle: RePEc:bla:scjsta:v:33:y:2006:i:4:p:651-671
    DOI: 10.1111/j.1467-9469.2006.00513.x
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    Cited by:

    1. Arribas-Gil Ana, 2010. "Parameter Estimation in Multiple-Hidden I.I.D. Models from Biological Multiple Alignment," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 9(1), pages 1-37, January.
    2. Arribas-Gil Ana & Matias Catherine, 2012. "A Context Dependent Pair Hidden Markov Model for Statistical Alignment," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(1), pages 1-29, January.
    3. Arribas-Gil Ana & Matias Catherine, 2017. "A time warping approach to multiple sequence alignment," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 16(2), pages 133-144, April.

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