Distortions of multivariate risk measures: a level-sets based approach
AbstractIn this paper, we propose a parametric model for multivariate distributions. The model is based on distortion functions, i.e. some transformations of a multivariate distribution which permit to generate new families of multivariate distribution functions. We derive some properties of considered distortions. A suitable proximity indicator between level curves is introduced in order to evaluate the quality of candidate distortion parameters. Using this proximity indicator and properties of distorted level curves, we give a specific estimation procedure. The estimation algorithm is mainly relying on straightforward univariate optimizations, and we finally get parametric representations of both multivariate distribution functions and associated level curves. Our results are motivated by applications in multivariate risk theory. The methodology is illustrated on real examples.
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 InfoPaper provided by HAL in its series Working Papers with number hal-00756387.
Date of creation: 12 Nov 2012
Date of revision:
Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00756387
Contact details of provider:
Web page: http://hal.archives-ouvertes.fr/
Multivariate probability distortions; Level sets estimation ; Iterated compositions; Hyperbolic conversion functions ; Multivariate risk measures.;
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.:
- Biernacki, Christophe & Celeux, Gilles & Govaert, Gerard, 2003. "Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 561-575, January.
- Chacón, José E. & Rodríguez-Casal, Alberto, 2010. "A note on the universal consistency of the kernel distribution function estimator," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1414-1419, September.
- Alexis Bienven�e & Didier Rulli�re, 2012. "Iterative Adjustment of Survival Functions by Composed Probability Distortions," The Geneva Risk and Insurance Review, Palgrave Macmillan, vol. 37(2), pages 156-179, September.
- Belzunce, F. & Castano, A. & Olvera-Cervantes, A. & Suarez-Llorens, A., 2007. "Quantile curves and dependence structure for bivariate distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 5112-5129, June.
- Dehaan, L. & Huang, X., 1995. "Large Quantile Estimation in a Multivariate Setting," Journal of Multivariate Analysis, Elsevier, vol. 53(2), pages 247-263, May.
- Embrechts, Paul & Puccetti, Giovanni, 2006. "Bounds for functions of multivariate risks," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 526-547, February.
- Valdez, Emiliano A., 2009. "On the Distortion of a Copula and its Margins," MPRA Paper 20524, University Library of Munich, Germany.
- Areski Cousin & Elena Di Bernadino, 2013. "On Multivariate Extensions of Value-at-Risk," Working Papers hal-00638382, HAL.
- Obereder, Andreas & Scherzer, Otmar & Kovac, Arne, 2007. "Bivariate density estimation using BV regularisation," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5622-5634, August.
- Areski Cousin & Elena Di Bernadino, 2011. "On Multivariate Extensions of Value-at-Risk," Papers 1111.1349, arXiv.org, revised Apr 2013.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD).
If references are entirely missing, you can add them using this form.