The Annals of Statistics

Asymptotic normality of the maximum likelihood estimator in state space models

Jens Ledet Jensen and Niels Væver Petersen

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State space models is a very general class of time series models capable of modelling dependent observations in a natural and interpretable way. Inference in such models has been studied by Bickel, Ritov and Rydén, who consider hidden Markov models, which are special kinds of state space models, and prove that the maximum likelihood estimator is asymptotically normal under mild regularity conditions. In this paper we generalize the results of Bickel, Ritov and Rydén to state space models, where the latent process is a continuous state Markov chain satisfying regularity conditions, which are fulfilled if the latent process takes values in a compact space.

Article information

Ann. Statist., Volume 27, Number 2 (1999), 514-535.

First available in Project Euclid: 5 April 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F12: Asymptotic properties of estimators
Secondary: 62M09: Non-Markovian processes: estimation

State space models asymptotic normality maximum likelihood estimation.


Jensen, Jens Ledet; Petersen, Niels Væver. Asymptotic normality of the maximum likelihood estimator in state space models. Ann. Statist. 27 (1999), no. 2, 514--535. doi:10.1214/aos/1018031205.

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