Statistics/Probability Theory
Maximum likelihood estimation for hidden semi-Markov models
Comptes Rendus. Mathématique, Volume 342 (2006) no. 3, pp. 201-205.

In this Note we consider a discrete-time hidden semi-Markov model and we prove that the nonparametric maximum likelihood estimators for the characteristics of such a model have nice asymptotic properties, namely consistency and asymptotic normality.

Dans cette Note nous introduisons un modèle semi-markovien caché à temps discret et nous prouvons que les estimateurs du maximum de vraisemblance non-paramétrique d'un tel modèle ont de bonnes propriétés asymptotiques, à savoir la convergence et la normalité asymptotique.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2005.12.013
Barbu, Vlad 1; Limnios, Nikolaos 1

1 Laboratoire de mathématiques appliquées de Compiègne, Université de technologie de Compiègne, BP 20529, 60205 Compiègne, France
@article{CRMATH_2006__342_3_201_0,
     author = {Barbu, Vlad and Limnios, Nikolaos},
     title = {Maximum likelihood estimation for hidden {semi-Markov} models},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {201--205},
     publisher = {Elsevier},
     volume = {342},
     number = {3},
     year = {2006},
     doi = {10.1016/j.crma.2005.12.013},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2005.12.013/}
}
TY  - JOUR
AU  - Barbu, Vlad
AU  - Limnios, Nikolaos
TI  - Maximum likelihood estimation for hidden semi-Markov models
JO  - Comptes Rendus. Mathématique
PY  - 2006
SP  - 201
EP  - 205
VL  - 342
IS  - 3
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2005.12.013/
DO  - 10.1016/j.crma.2005.12.013
LA  - en
ID  - CRMATH_2006__342_3_201_0
ER  - 
%0 Journal Article
%A Barbu, Vlad
%A Limnios, Nikolaos
%T Maximum likelihood estimation for hidden semi-Markov models
%J Comptes Rendus. Mathématique
%D 2006
%P 201-205
%V 342
%N 3
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2005.12.013/
%R 10.1016/j.crma.2005.12.013
%G en
%F CRMATH_2006__342_3_201_0
Barbu, Vlad; Limnios, Nikolaos. Maximum likelihood estimation for hidden semi-Markov models. Comptes Rendus. Mathématique, Volume 342 (2006) no. 3, pp. 201-205. doi : 10.1016/j.crma.2005.12.013. http://www.numdam.org/articles/10.1016/j.crma.2005.12.013/

[1] Barbu, V.; Boussemart, M.; Limnios, N. Discrete time semi-Markov model for reliability and survival analysis, Comm. Statist. Theory Methods, Volume 33 (2004) no. 11, pp. 2833-2868

[2] Barbu, V.; Limnios, N. Discrete time semi-Markov processes for reliability and survival analysis – a nonparametric estimation approach (Nikulin, M.; Balakrishnan, N.; Meshbah, M.; Limnios, N., eds.), Parametric and Semiparametric Models with Applications to Reliability, Survival Analysis and Quality of Life, Birkhäuser, Boston, 2004, pp. 487-502

[3] Baum, L.E.; Petrie, T. Statistical inference for probabilistic functions of finite state Markov chains, Ann. Math. Statist., Volume 37 (1966), pp. 1554-1563

[4] Bickel, P.J.; Ritov, Y.; Rydén, T. Asymptotic normality of the maximum-likelihood estimator for general hidden Markov models, Ann. Statist., Volume 26 (1998), pp. 1614-1635

[5] Churchill, G. Hidden Markov chains and the analysis of genome structure, Computers Chem., Volume 16 (1992), pp. 107-115

[6] R. Douc, Non singularity of the asymptotic Fisher information matrix in hidden Markov models, École Polytechnique, Preprint

[7] Douc, R.; Matias, C. Asymptotics of the maximum likelihood estimator for general hidden Markov models, Bernoulli, Volume 7 (2001) no. 3, pp. 381-420

[8] Douc, R.; Moulines, E.; Rydén, T. Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime, Ann. Statist., Volume 32 (2004) no. 5, pp. 2254-2304

[9] J.D. Ferguson, Variable duration models for speech, in: Proc. of the Symposium on the Application of Hidden Markov Models to Text and Speech, Princeton, NJ, 1980, pp. 143–179

[10] Guédon, Y. Estimating hidden semi-Markov chains from discrete sequences, J. Comput. Graph. Statist., Volume 12 (2003) no. 3, pp. 604-639

[11] Guédon, Y.; Cocozza-Thivent, C. Explicit state occupancy modelling by hidden semi-Markov models: application of Derin's scheme, Computer Speech and Language, Volume 4 (1990), pp. 167-192

[12] Jensen, J.L.; Petersen, N.V. Asymptotic normality of the maximum likelihood estimator in state space models, Ann. Statist., Volume 27 (1999), pp. 514-535

[13] Leroux, B.G. Maximum-likelihood estimation for hidden Markov models, Stochastic Process. Appl., Volume 40 (1992), pp. 127-143

[14] Limnios, N.; Oprişan, G. Semi-Markov Processes and Reliability, Birkhäuser, Boston, 2001

[15] F. Muri-Majoube, Comparaison d'algorithmes d'identification de Chaînes de Markov Cachées et application à la détection de régions homogènes dans les séquences d'ADN, Ph.D. Thesis, University Paris 5, 1997

[16] Rabiner, L.R. A tutorial on hidden Markov models and selected applications in speech recognition, Proc. IEEE, Volume 77 (1989), pp. 257-284

[17] Sansom, J.; Thomson, P.J. Fitting hidden semi-Markov models to breakpoint rainfall data, J. Appl. Probab., Volume 38A (2001), pp. 142-157

Cited by Sources: