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Asymptotic normality of M-estimators in nonhomogeneous hidden Markov models

Part of: Parametric inference Inference from stochastic processes

Published online by Cambridge University Press:  14 July 2016

Jens Ledet Jensen
Jens Ledet Jensen*
Affiliation:
University of Aarhus, Department of Mathematical Sciences, University of Aarhus, Ny Munkegade Building 1530, DK-8000 Aarhus C, Denmark. Email address: [email protected]
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Abstract

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Results on asymptotic normality for the maximum likelihood estimate in hidden Markov models are extended in two directions. The stationarity assumption is relaxed, which allows for a covariate process influencing the hidden Markov process. Furthermore, a class of estimating equations is considered instead of the maximum likelihood estimate. The basic ingredients are mixing properties of the process and a general central limit theorem for weakly dependent variables.

Keywords

Estimating equationmixing properties

MSC classification

Primary: 62F12: Asymptotic properties of estimators
Secondary: 62M09: Non-Markovian processes
Type
Part 6. Statistics
Information
Journal of Applied Probability , Volume 48 , Issue A: New Frontiers in Applied Probability (Journal of Applied Probability Special Volume 48A) , August 2011 , pp. 295 - 306
Copyright
Copyright © Applied Probability Trust 2011 

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