[Estimation du maximum de vraisemblance d'un modèle semi-markovien caché]
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.
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.
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@article{CRMATH_2006__342_3_201_0,
author = {Vlad Barbu and Nikolaos Limnios},
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},
}
Vlad Barbu; Nikolaos Limnios. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.12.013/
[1] Discrete time semi-Markov model for reliability and survival analysis, Comm. Statist. Theory Methods, Volume 33 (2004) no. 11, pp. 2833-2868
[2] Discrete time semi-Markov processes for reliability and survival analysis – a nonparametric estimation approach (M. Nikulin; N. Balakrishnan; M. Meshbah; N. Limnios, eds.), Parametric and Semiparametric Models with Applications to Reliability, Survival Analysis and Quality of Life, Birkhäuser, Boston, 2004, pp. 487-502
[3] Statistical inference for probabilistic functions of finite state Markov chains, Ann. Math. Statist., Volume 37 (1966), pp. 1554-1563
[4] Asymptotic normality of the maximum-likelihood estimator for general hidden Markov models, Ann. Statist., Volume 26 (1998), pp. 1614-1635
[5] 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] Asymptotics of the maximum likelihood estimator for general hidden Markov models, Bernoulli, Volume 7 (2001) no. 3, pp. 381-420
[8] 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] Estimating hidden semi-Markov chains from discrete sequences, J. Comput. Graph. Statist., Volume 12 (2003) no. 3, pp. 604-639
[11] 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] Asymptotic normality of the maximum likelihood estimator in state space models, Ann. Statist., Volume 27 (1999), pp. 514-535
[13] Maximum-likelihood estimation for hidden Markov models, Stochastic Process. Appl., Volume 40 (1992), pp. 127-143
[14] 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] A tutorial on hidden Markov models and selected applications in speech recognition, Proc. IEEE, Volume 77 (1989), pp. 257-284
[17] Fitting hidden semi-Markov models to breakpoint rainfall data, J. Appl. Probab., Volume 38A (2001), pp. 142-157
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