Estimation of extreme risk regions under multivariate regular variation
Abstract
When considering d possibly dependent random variables, one is often interested in extreme risk regions, with very small probability p. We consider risk regions of the form , where f is the joint density and a small number. Estimation of such an extreme risk region is difficult since it contains hardly any or no data. Using extreme value theory, we construct a natural estimator of an extreme risk region and prove a refined form of consistency, given a random sample of multivariate regularly varying random vectors. In a detailed simulation and comparison study, the good performance of the procedure is demonstrated. We also apply our estimator to financial data.
Cite
@article{arxiv.1211.5239,
title = {Estimation of extreme risk regions under multivariate regular variation},
author = {Juan-Juan Cai and John H. J. Einmahl and Laurens de Haan},
journal= {arXiv preprint arXiv:1211.5239},
year = {2012}
}
Comments
Published in at http://dx.doi.org/10.1214/11-AOS891 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)