Maximum likelihood estimator for hidden Markov models in continuous time

Pavel Chigansky

doi:10.1007/s11203-008-9025-4

Maximum likelihood estimator for hidden Markov models in continuous time

Pavel Chigansky^*

^*Corresponding author for this work

Department of Statistics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

The paper studies large sample asymptotic properties of the Maximum Likelihood Estimator (MLE) for the parameter of a continuous time Markov chain, observed in white noise. Using the method of weak convergence of likelihoods due to Ibragimov and Khasminskii (Statistical estimation, vol 16 of Applications of mathematics. Springer-Verlag, New York), consistency, asymptotic normality and convergence of moments are established for MLE under certain strong ergodicity assumptions on the chain.

Original language	English
Pages (from-to)	139-163
Number of pages	25
Journal	Statistical Inference for Stochastic Processes
Volume	12
Issue number	2
DOIs	https://doi.org/10.1007/s11203-008-9025-4
State	Published - Jun 2009

Keywords

Continuous time hidden Markov models
Filtering
Maximum Likelihood estimator
Partial observations

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10.1007/s11203-008-9025-4

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AB - The paper studies large sample asymptotic properties of the Maximum Likelihood Estimator (MLE) for the parameter of a continuous time Markov chain, observed in white noise. Using the method of weak convergence of likelihoods due to Ibragimov and Khasminskii (Statistical estimation, vol 16 of Applications of mathematics. Springer-Verlag, New York), consistency, asymptotic normality and convergence of moments are established for MLE under certain strong ergodicity assumptions on the chain.

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KW - Filtering

KW - Maximum Likelihood estimator

KW - Partial observations

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Maximum likelihood estimator for hidden Markov models in continuous time

Abstract

Keywords

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