Hidden Markov model likelihoods and their derivatives behave like i.i.d. ones
Annales de l'I.H.P. Probabilités et statistiques, Volume 38 (2002) no. 6, p. 825-846
@article{AIHPB_2002__38_6_825_0,
     author = {Bickel, Peter J. and Ritov, Ya'acov and Ryd\'en, Tobias},
     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},
     publisher = {Elsevier},
     volume = {38},
     number = {6},
     year = {2002},
     pages = {825-846},
     zbl = {1011.62087},
     mrnumber = {1955339},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2002__38_6_825_0}
}
Hidden Markov model likelihoods and their derivatives behave like i.i.d. ones. Annales de l'I.H.P. Probabilités et statistiques, Volume 38 (2002) no. 6, pp. 825-846. http://www.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 1010226 | Zbl 0672.62024

[2] L.E. Baum, T. Petrie, Statistical inference for probabilistic functions of finite state Markov chains, Ann. Math. Statist. 37 (1966) 1554-1563. | MR 202264 | Zbl 0144.40902

[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 822063

[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 0727.62035

[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 1416863 | Zbl 1066.62535

[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 1647705 | Zbl 0932.62097

[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 2102510

[9] P. Doukhan, Mixing. Properties and Examples, Lecture Notes in Statistics, 85, Springer-Verlag, New York, 1994. | MR 1312160 | Zbl 0801.60027

[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 958209 | Zbl 0655.62015

[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 1714719 | Zbl 0952.62023

[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 1145463 | Zbl 0738.62081

[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 676213 | Zbl 0488.62018

[17] I.L. Macdonald, W. Zucchini, Hidden Markov and Other Models for Discrete-valued Time Series, Chapman and Hall, London, 1997. | MR 1692202 | Zbl 0868.60036

[18] I. Meilijson, A fast improvement to the EM algorithm on its own terms, J. Roy. Statist. Soc. B 51 (1989) 127-138. | MR 984999 | Zbl 0674.65118

[19] T. Petrie, Probabilistic functions of finite state Markov chains, Ann. Math. Statist. 40 (1969) 97-115. | MR 239662 | Zbl 0181.21201

[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 1171883 | Zbl 0744.60028