The likelihood ratio test for the number of components in a mixture with Markov regime
ESAIM: Probability and Statistics, Volume 4 (2000), pp. 25-52.
@article{PS_2000__4__25_0,
     author = {Gassiat, Elisabeth and Keribin, Christine},
     title = {The likelihood ratio test for the number of components in a mixture with {Markov} regime},
     journal = {ESAIM: Probability and Statistics},
     pages = {25--52},
     publisher = {EDP-Sciences},
     volume = {4},
     year = {2000},
     zbl = {0982.62016},
     mrnumber = {1780964},
     language = {en},
     url = {http://www.numdam.org/item/PS_2000__4__25_0/}
}
TY  - JOUR
AU  - Gassiat, Elisabeth
AU  - Keribin, Christine
TI  - The likelihood ratio test for the number of components in a mixture with Markov regime
JO  - ESAIM: Probability and Statistics
PY  - 2000
DA  - 2000///
SP  - 25
EP  - 52
VL  - 4
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/PS_2000__4__25_0/
UR  - https://zbmath.org/?q=an%3A0982.62016
UR  - https://www.ams.org/mathscinet-getitem?mr=1780964
LA  - en
ID  - PS_2000__4__25_0
ER  - 
%0 Journal Article
%A Gassiat, Elisabeth
%A Keribin, Christine
%T The likelihood ratio test for the number of components in a mixture with Markov regime
%J ESAIM: Probability and Statistics
%D 2000
%P 25-52
%V 4
%I EDP-Sciences
%G en
%F PS_2000__4__25_0
Gassiat, Elisabeth; Keribin, Christine. The likelihood ratio test for the number of components in a mixture with Markov regime. ESAIM: Probability and Statistics, Volume 4 (2000), pp. 25-52. http://www.numdam.org/item/PS_2000__4__25_0/

[1] L.D. Atwood, A.F. Wilson, J.E. Bailey-Wilson, J.N. Carruth and R.C. Elston, On the distribution of the likelihood ratio test statistic for a mixture of two normal distributions. Comm. Statist. Simulation Comput. 25 ( 1996) 733-740. | MR | Zbl

[2] L.E. Baum and T. Petrie, Statistical inference for probabilistic functions of finite state Markov chains. Ann. Math. Stat. 37 ( 1966) 1554-1563. | MR | Zbl

[3] P.J. Bickel and Y. Ritov, Inference in hidden Markov models I: Local asymptotic normality in the stationary case. Bernoulli 2 ( 1996) 199-228. | MR | Zbl

[4] P.J. Bickel, Y. Ritov and T. Ryden, Asymptotic normality of the maximum-likelihood estimator for general hidden Markov models. Annals of Stat. 26 ( 1998) 614-1635. | MR | Zbl

[5] R.-J. Chuang and N.R. Mendell, The approximate null distribution of the likelihood ratio test for a mixture of two bivariate normal distributions with equal covariance. Comm. Statist. Simulation Comput. 26 ( 1997) 631-648. | MR | Zbl

[6] G.A. Churchill, Stochastic models for heterogeneous DNA sequences. Bull. Math. Biology 51 ( 1989) 79-94. | MR | Zbl

[7] G. Ciuperca, Sur le test de maximum de vraisemblance pour le mélange de populations. Note aux C.R.A.S., 328, Série I, 4 ( 1999) 351-358. | MR | Zbl

[8] D. Dacunha-Castelle and M. Duflo, Probabilits et statistiques, Tome 2. Masson ( 1993). | MR | Zbl

[9] D. Dacunha-Castelle and E. Gassiat, Estimation of the number of components in a mixture. Bernoulli 3 ( 1997a) 279-299. | MR | Zbl

[10] D. Dacunha-Castelle and E. Gassiat, Testing in locally conic models. ESAIM Probab. Statist. 1 ( 1997b). | Numdam | MR | Zbl

[11] D. Dacunha-Castelle and E. Gassiat, Testing the order of a model using locally conic parametrization: Population mixtures and stationary ARMA processes. Ann. Statist. 27 ( 1999) 1178-1209. | MR | Zbl

[12] A.P. Dempster, N.M. Laird and D.B. Rubin, Large Maximum-likelihood from incomplete data via the EM algorithm. J. Roy. Statist. Soc. Ser. B 39 ( 1977) 1-38. | MR | Zbl

[13] R. Douc and C. Matias, Asymptotics of the Maximum Likelihood Estimator for general Hidden Markov Models ( 1999) (submitted). | Zbl

[14] M. Duflo, Algorithmes stochastiques. Springer ( 1996). | MR | Zbl

[15] Z.D. Feng and C.E. Mcculloch, Using bootstrap Likelihood Ratio in Finite Mixture Models. J. Roy. Statist. Soc. Ser. B 58 ( 1996) 609-617. | Zbl

[16] L. Finesso, Consistent Estimation of the Order for Markov and Hidden Markov Chains. Ph.D. Thesis, University of Maryland ( 1990).

[17] D.R. Fredkin and J.A. Rice, Maximum likelihood estimation and identification directly from single-channel recordings. Proc. Roy. Soc. London Ser. B 249 ( 1992) 125-132.

[18] P. Hall and C.C. Heyde, Martingale Limit Theory and Its Application. Academic Press ( 1980). | MR | Zbl

[19] J.A. Hartigan, A failure of likelihood ratio asymptotics for normal mixtures, in Proc. Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer, edited by L.M. Le Cam and R.A. Olshen ( 1985) 807-810. | MR

[20] J. Henna, On estimating the number of constituents of a finite mixture of continuous distributions. Ann. Inst. Statist. Math. 37 ( 1985) 235-240. | MR | Zbl

[21] J.L. Jensen and N.V. Petersen, Asymptotic normality of the maximum likelihood estimator in state space models. Ann. Statist. 27 ( 1999) 514-535. | MR | Zbl

[22] C. Keribin, Tests de modèles par maximum de vraisemblance, Thèse de l'Université d'Evry-Val d'Essonne ( 1999).

[23] C. Keribin, Consistent estimation of the Order of Mixture Models ( 1997) (submitted). | Zbl

[24] B.G. Leroux, Maximum-likelihood estimation for hidden Markov models. Stochastic Process Appl. 40 ( 1992) 127-143. | MR | Zbl

[25] B.G. Leroux and M.L. Puterman, Maximum Penalized Likelihood Estimation for Independent and Markov-Dependent Mixture Models. Biometrics 48 ( 1992) 545-558.

[26] B.G. Lindsay, Mixture models: Theory, Geometry and Applications ( 1995). | Zbl

[27] I.L. Mac Donald and W. Zucchini, Hidden Markov and Other Models for Discrete-valued Time Series. Chapman and Hall ( 1997). | MR | Zbl

[28] G.J. Mclachlan, On Bootstrapping the Likelihood Ratio Test Statistic for the Number of Components in a Normal Mixture. Appl. Statist. 36 ( 1987) 318-324.

[29] L. Mevel, Statistique asymptotique pour les modèles de Markov cachés. Thèse de l'Université de Rennes I ( 1997).

[30] L. Mevel and F. Legland, Exponential forgetting and Geometrie Ergodicity in Hidden Markov models. Math. Control Signals Systems (to appear). | MR | Zbl

[31] S.P. Meyn and R.L. Tweedie, Markov chains and stochastic stability. Springer-Verlag ( 1993). | MR | Zbl

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

[33] T. Ryden, Estimating the order of hidden Markov models. Statistics 26 ( 1995) 345-354. | MR | Zbl

[34] P. Vandekerkhove, Identification de l'ordre des processus ARMA stables. Contribution à l'étude statistique des chaînes de Markov cachées. Thèse de l'Université de Montpellier II ( 1997).

[35] A. Van Der Vaart, Asymptotic Statistics. Cambridge Ed. ( 1999). | MR | Zbl