A contrast estimator for completely or partially observed hypoelliptic diffusion

Parametric estimation of two-dimensional hypoelliptic diffusions is considered when complete observations–both coordinates discretely observed–or partial observations–only one coordinate observed–are available. Since the volatility matrix is degenerate, Euler contrast estimators cannot be used direc...

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Bibliographic Details
Published in:Stochastic processes and their applications 2012-07, Vol.122 (7), p.2521-2552
Main Authors: Samson, Adeline, Thieullen, Michèle
Format: Article
Language:English
Subjects:
Contrast estimator
Hypoelliptic diffusion
Langevin system
Mathematics
Partial observations
Statistics
Statistics Theory
Stochastic differential equations
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Summary:Parametric estimation of two-dimensional hypoelliptic diffusions is considered when complete observations–both coordinates discretely observed–or partial observations–only one coordinate observed–are available. Since the volatility matrix is degenerate, Euler contrast estimators cannot be used directly. For complete observations, we introduce an Euler contrast based on the second coordinate only. For partial observations, we define a contrast based on an integrated diffusion resulting from a transformation of the original one. A theoretical study proves that the estimators are consistent and asymptotically Gaussian. A numerical application to Langevin systems illustrates the nice properties of both complete and partial observations’ estimators.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2012.04.006