## Maximum-likelihood estimation for hidden Markov models.(English)Zbl 0738.62081

Summary: Hidden Markov models assume a sequence of random variables to be conditionally independent given a sequence of state variables which forms a Markov chain. Maximum-likelihood estimation for these models can be performed using the EM algorithm. The consistency of a sequence of maximum-likelihood estimators is proved. Also, the conclusion of the Shannon-McMillan-Breiman theorem on entropy convergence is established for hidden Markov models.

### MSC:

 62M05 Markov processes: estimation; hidden Markov models 62F12 Asymptotic properties of parametric estimators 62M09 Non-Markovian processes: estimation
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### References:

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