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Statistics
A Journal of Theoretical and Applied Statistics
Volume 26, 1995 - Issue 4
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Original Articles

Estimating the Order of Hidden Markov Models

Pages 345-354 | Received 11 Aug 1993, Accepted 18 Jul 1994, Published online: 27 Jun 2007

References

  • Akaike , H. 1974 . A new look at the statistical model identification . IEEE Trans. Auto. Control , 19 : 716 – 723 .
  • Baum , L. E. and Petrie , T. 1966 . Statistical inference for probabilistic functions of finite state Markov chains . Ann. Math. Statist. , 37 : 1554 – 1563 .
  • Bickel , P. J. and Ritov , Y. “ Inference in hidden Markov models I. Local asymptotic normality in the stationary case ” . Preprint
  • Donoho , D. L. 1988 . One-sided inference about functionals of a density . Ann. Statist. , 16 : 1390 – 1420 .
  • Everitt , B. S. and Hand , D. J. 1981 . Finite Mixture Distributions , Chapman and Hall .
  • Fredkin , D. R. and Rice , J. A. 1992 . Maximum likelihood estimation and identification directly from single-channel recordings . Proc. Royal Soc. Lond. B , 249 : 125 – 132 .
  • Gilbert , E. J. 1959 . On the identifiability problem for functions of finite Markov chains . Ann. Math. Statist. , 30 : 688 – 697 .
  • Henna , J. 1985 . On estimating of the number of constituents of a finite mixture of continuous distributions . Ann. Inst. Statist. Math. , 37 : 235 – 240 .
  • Holst , U. and Lindgren , G. 1991 . Recursive estimation in mixture models with Markov regime . IEEE Trans. Inform. Theory , IT-37 : 1683 – 1690 .
  • Leroux , B. G. 1992 . Consistent estimation of a mixing distribution . Ann. Statist. , 20 : 1350 – 1360 .
  • Leroux , B. G. 1992 . Maximum-likelihood estimation for hidden Markov models . Stoch. Proc. Appl. , 40 : 127 – 143 .
  • Leroux , B. G. and Puterman , M. L. 1992 . Maximum-penalized-likelihood estimation for independent and Markov-dependent mixture models . Biometrics , 48 : 545 – 558 .
  • Lindgren , G. 1978 . Markov regime models for mixed distributions and switching regressions . Scand. J. Statist. , 5 : 81 – 91 .
  • McLachlan , G. J. 1987 . On bootstrapping the likelihood ratio test statistic for the number of components in a normal mixture . Appl. Statist. , 36 : 318 – 324 .
  • McLachlan , G. J. and Basford , K. E. 1988 . Mixture Models , Marcel Dekker .
  • Petrie , T. 1969 . Probabilistic functions of finite state Markov chains . Ann. Math. Statist. , 40 : 97 – 115 .
  • Press , W. H. , Flannery , B. P. , Teukolsky , S. A. and Vetterling , W. T. 1989 . Numerical Recipes , Cambridge University Press .
  • Rabiner , L. R. 1989 . A tutorial on hidden Markov models and selected applications in speech recognition . Proc. IEEE , 77 : 257 – 284 .
  • Rydén , T. 1994 . Consistent and asymptotically normal parameter estimates for hidden Markov models . Ann. Statist. , 22 : 1884 – 1895 .
  • Schwarz , G. 1978 . Estimating the dimension of a model . Ann. Statist. , 6 : 461 – 464 .
  • Smith , B. R. 1993 . Mixture estimation and the neurophysiological quantal hypothesis . Biometrics , 49 : 643 – 651 .
  • Soromenho , G. 1994 . Comparing approaches for testing the number of components in a finite mixture model . Comp. Statist. , 9 : 65 – 78 .
  • Teicher , H. 1967 . Identifiability of mixtures of product measures . Ann. Math. Statist. , 38 : 1300 – 1302 .
  • Titterington , D. M. 1990 . Some recent research in the analysis of mixture distributions . Statistics , 21 : 619 – 641 .
  • Titterington , D. M. , Smith , A. F. M. and Makov , U. E. 1985 . Statistical Analysis of Finite Mixture Distributions , Wiley .

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