1. Analyticity, Convergence, and Convergence Rate of Recursive Maximum-Likelihood Estimation in Hidden Markov Models.
- Author
-
Tadic, Vladislav B.
- Subjects
MATHEMATICAL analysis ,STOCHASTIC convergence ,MAXIMUM likelihood statistics ,ESTIMATION theory ,HIDDEN Markov models ,ASYMPTOTES ,MATHEMATICAL inequalities - 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]
- Published
- 2010
- Full Text
- View/download PDF