A contrast estimator for completely or partially observed hypoelliptic diffusion
AbstractParametric 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by Elsevier in its journal Stochastic Processes and their Applications.
Volume (Year): 122 (2012)
Issue (Month): 7 ()
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
- Benjamin Favetto & Adeline Samson, 2010. "Parameter Estimation for a Bidimensional Partially Observed Ornstein-Uhlenbeck Process with Biological Application," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 37(2), pages 200-220.
- Susanne Ditlevsen & Michael Sørensen, 2004. "Inference for Observations of Integrated Diffusion Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 31(3), pages 417-429.
- Mattingly, J. C. & Stuart, A. M. & Higham, D. J., 2002. "Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise," Stochastic Processes and their Applications, Elsevier, vol. 101(2), pages 185-232, October.
- Arnaud Gloter, 2006. "Parameter Estimation for a Discretely Observed Integrated Diffusion Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 33(1), pages 83-104.
- Yvo Pokern & Andrew M. Stuart & Petter Wiberg, 2009. "Parameter estimation for partially observed hypoelliptic diffusions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 49-73.
If references are entirely missing, you can add them using this form.