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Analyticity, Convergence, and Convergence Rate of Recursive Maximum-Likelihood Estimation in Hidden Markov Models.
- Source :
- IEEE Transactions on Information Theory; 12/01/2010, Vol. 56 Issue 12, p6406-6432, 27p
- Publication Year :
- 2010
-
Abstract
- This paper considers the asymptotic properties of the recursive maximum-likelihood estimator for hidden Markov models. The paper is focused on the analytic properties of the asymptotic log-likelihood and on the point-convergence and convergence rate of the recursive maximum-likelihood estimator. Using the principle of analytic continuation, the analyticity of the asymptotic log-likelihood is shown for analytically parameterized hidden Markov models. Relying on this fact and some results from differential geometry (Lojasiewicz inequality), the almost sure point convergence of the recursive maximum-likelihood algorithm is demonstrated, and relatively tight bounds on the convergence rate are derived. As opposed to the existing result on the asymptotic behavior of maximum-likelihood estimation in hidden Markov models, the results of this paper are obtained without assuming that the log-likelihood function has an isolated maximum at which the Hessian is strictly negative definite. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 56
- Issue :
- 12
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 55353633
- Full Text :
- https://doi.org/10.1109/TIT.2010.2081110