Hidden Markov model likelihoods and their derivatives behave like i.i.d. ones
Peter J. Bickel; Ya'acov Ritov; Tobias Rydén
Annales de l'I.H.P. Probabilités et statistiques (2002)
- Volume: 38, Issue: 6, page 825-846
- ISSN: 0246-0203
Access Full Article
topHow to cite
topReferences
top- [1] O. Barndorff-Nielsen, D.R. Cox, Asymptotic Techniques for Use in Statistics, Chapman and Hall, London, 1989. Zbl0672.62024MR1010226
- [2] L.E. Baum, T. Petrie, Statistical inference for probabilistic functions of finite state Markov chains, Ann. Math. Statist.37 (1966) 1554-1563. Zbl0144.40902MR202264
- [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. MR822063
- [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. Zbl0727.62035
- [5] P.J. Bickel, Y. Ritov, Inference in hidden Markov models I: Local asymptotic normality in the stationary case, Bernoulli2 (1996) 199-228. Zbl1066.62535MR1416863
- [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. Zbl0932.62097MR1647705
- [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. Zbl1011.62087
- [8] R. Douc, E. Moulines, T. Rydén, Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime, Preprint, 2001. Zbl1056.62028MR2102510
- [9] P. Doukhan, Mixing. Properties and Examples, Lecture Notes in Statistics, 85, Springer-Verlag, New York, 1994. Zbl0801.60027MR1312160
- [10] D.R. Fredkin, J.A. Rice, Maximum likelihood estimation and identification directly from single-channel recordings, Proc. Roy. Soc. London B249 (1992) 125-132.
- [11] P. Hall, Rate of convergence in bootstrap approximations, Ann. Probab.16 (1988) 1665-1684. Zbl0655.62015MR958209
- [12] J.L. Jensen, N.V. Petersen, Asymptotic normality of the maximum likelihood estimator in state space models, Ann. Statist.27 (1999) 514-535. Zbl0952.62023MR1714719
- [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. Zbl0738.62081MR1145463
- [15] B.G. Leroux, M.L. Puterman, Maximum-penalized-likelihood estimation for independent and Markov-dependent mixture models, Biometrics48 (1992) 545-558.
- [16] T.A. Louis, Finding the observed information matrix when using the EM algorithm, J. Roy. Statist. Soc. B44 (1982) 226-233. Zbl0488.62018MR676213
- [17] I.L. MacDonald, W. Zucchini, Hidden Markov and Other Models for Discrete-valued Time Series, Chapman and Hall, London, 1997. Zbl0868.60036MR1692202
- [18] I. Meilijson, A fast improvement to the EM algorithm on its own terms, J. Roy. Statist. Soc. B51 (1989) 127-138. Zbl0674.65118MR984999
- [19] T. Petrie, Probabilistic functions of finite state Markov chains, Ann. Math. Statist.40 (1969) 97-115. Zbl0181.21201MR239662
- [20] L.R. Rabiner, A tutorial on hidden Markov models and selected applications in speech recognition, Proc. IEEE77 (1989) 257-284.
- [21] L. Saulis, V.A. Statulevičius, Limit Theorems for Large Deviations, Kluwer, Dordrecht, 1991. Zbl0744.60028MR1171883