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June 2011 Estimation of extreme risk regions under multivariate regular variation
Juan-Juan Cai, John H. J. Einmahl, Laurens de Haan
Ann. Statist. 39(3): 1803-1826 (June 2011). DOI: 10.1214/11-AOS891

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 {z ∈ ℝd : f(z) ≤ β}, where f is the joint density and β 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.

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Juan-Juan Cai. John H. J. Einmahl. Laurens de Haan. "Estimation of extreme risk regions under multivariate regular variation." Ann. Statist. 39 (3) 1803 - 1826, June 2011. https://doi.org/10.1214/11-AOS891

Information

Published: June 2011
First available in Project Euclid: 25 July 2011

zbMATH: 1221.62075
MathSciNet: MR2850221
Digital Object Identifier: 10.1214/11-AOS891

Subjects:
Primary: 62G05, 62G07, 62G32
Secondary: 60F05, 60G70

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 3 • June 2011
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