Hidden Markov model likelihoods and their derivatives behave like i.i.d. ones
Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002) no. 6, pp. 825-846. 
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     title = {Hidden {Markov} model likelihoods and their derivatives behave like i.i.d. ones},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {825--846},
     publisher = {Elsevier},
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     mrnumber = {1955339},
     zbl = {1011.62087},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPB_2002__38_6_825_0/}
}
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Bickel, Peter J.; Ritov, Ya'acov; Rydén, Tobias. Hidden Markov model likelihoods and their derivatives behave like i.i.d. ones. Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002) no. 6, pp. 825-846. http://archive.numdam.org/item/AIHPB_2002__38_6_825_0/

[1] O. Barndorff-Nielsen, D.R. Cox, Asymptotic Techniques for Use in Statistics, Chapman and Hall, London, 1989. | MR | Zbl

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

[3] P.J. Bickel, F. Götze, W.R. Van Zwet, A simple analysis of third-order efficiency of estimates, in: Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer, Vol. II, Wadsworth, Belmont, CA, 1985, pp. 749-768. | MR

[4] P.J. Bickel, J.K. Ghosh, A decomposition for the likelihood ratio statistic and the Bartlett correction - A Bayesian argument, Ann. Statist. 18 (1990) 1070-1090. | Zbl

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

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

[7] P.J. Bickel, Y. Ritov, T. Rydén, Hidden Markov model likelihoods and their derivatives behave like i.i.d. ones: Details, Techical Report, 2002.

[8] R. Douc, E. Moulines, T. Rydén, Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime, Preprint, 2001. | MR

[9] P. Doukhan, Mixing. Properties and Examples, Lecture Notes in Statistics, 85, Springer-Verlag, New York, 1994. | MR | Zbl

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

[11] P. Hall, Rate of convergence in bootstrap approximations, Ann. Probab. 16 (1988) 1665-1684. | MR | Zbl

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

[13] R.E. Kalman, A new approach to linear filtering and prediction problems, in: Linear Least-Squares Estimation, Dowden, Hutchinson & Ross, Stroudsburg, PA, 1977, pp. 254-264.

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

[15] B.G. Leroux, M.L. Puterman, Maximum-penalized-likelihood estimation for independent and Markov-dependent mixture models, Biometrics 48 (1992) 545-558.

[16] T.A. Louis, Finding the observed information matrix when using the EM algorithm, J. Roy. Statist. Soc. B 44 (1982) 226-233. | MR | Zbl

[17] I.L. Macdonald, W. Zucchini, Hidden Markov and Other Models for Discrete-valued Time Series, Chapman and Hall, London, 1997. | MR | Zbl

[18] I. Meilijson, A fast improvement to the EM algorithm on its own terms, J. Roy. Statist. Soc. B 51 (1989) 127-138. | MR | Zbl

[19] T. Petrie, Probabilistic functions of finite state Markov chains, Ann. Math. Statist. 40 (1969) 97-115. | MR | Zbl

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

[21] L. Saulis, V.A. Statulevičius, Limit Theorems for Large Deviations, Kluwer, Dordrecht, 1991. | MR | Zbl