On recursive estimation for hidden Markov models
Hidden Markov models (HMMs) have during the last decade become a widespread tool for modelling sequences of dependent random variables. In this paper we consider a recursive estimator for HMMs based on the m-dimensional distribution of the process and show that this estimator converges to the set of stationary points of the corresponding Kullback-Leibler information. We also investigate averaging in this recursive scheme and show that conditional on convergence to the true parameter, and provided m is chosen large enough, the averaged estimator is close to optimal.
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Volume (Year): 66 (1997)
Issue (Month): 1 (February)
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References listed on IDEAS
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- Leroux, Brian G., 1992. "Maximum-likelihood estimation for hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 127-143, February.
- Schwabe, R., 1986. "Strong representation of an adaptive stochastic approximation procedure," Stochastic Processes and their Applications, Elsevier, vol. 23(1), pages 115-130, October.
- Rainer Schwabe & Harro Walk, 1996. "On a stochastic approximation procedure based on averaging," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 44(1), pages 165-180, December.
- Ma, D.-J. & Makowski, A.M. & Shwartz, A., 1990. "Stochastic approximations for finite-state Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 35(1), pages 27-45, June.