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Estimation of extreme risk regions under multivariate regular variation
Cai,J. Einmahl,J.H.J. de Haan,L.F.M.
Cai,J.
Einmahl,J.H.J.
de Haan,L.F.M.
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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2011
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einmal_AOS_2011.pdf
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Cai, J, Einmahl, J H J & de Haan, L F M 2011, 'Estimation of extreme risk regions under multivariate regular variation', Annals of Statistics, vol. 39, no. 3, pp. 1803-1826.