Geodesic
Maximum likelihood estimation for general hidden semi-Markov processes with backward recurrence time dependence
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 14–1, Tome 363 (2009), pp. 105-125

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This article concerns the study of the asymptotic properties of the maximum likelihood estimator (MLE) for the general hidden semi-Markov model (HSMM) with backward recurrence time dependence. By transforming the general HSMM into a general hidden Markov model, we prove that under some regularity conditions, the MLE is strongly consistent and asymptotically normal. We also provide useful expressions for the asymptotic covariance matrices, involving the MLE of the conditional sojourn times and the embedded Markov chain of the hidden semi-Markov chain. Bibl. – 17 titles. 
@article{ZNSL_2009_363_a5,
     author = {S. Trevezas and N. Limnios},
     title = {Maximum likelihood estimation for general hidden {semi-Markov} processes with backward recurrence time dependence},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {105--125},
     publisher = {mathdoc},
     volume = {363},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_363_a5/}
}
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S. Trevezas; N. Limnios. Maximum likelihood estimation for general hidden semi-Markov processes with backward recurrence time dependence. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 14–1, Tome 363 (2009), pp. 105-125. http://geodesic.mathdoc.fr/item/ZNSL_2009_363_a5/