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.
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@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://archive.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://archive.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://archive.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://archive.numdam.org/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 (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] 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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