Estimation of extreme risk regions under multivariate regular variation

By Juan-Juan Cai, John H. J. Einmahl, Laurens de Haan. 2011

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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 ∈ R d : 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.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/66c085e874d3c6098c40dd50f5605e754ed9d842

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Citations in the corpus

Living on the Multidimensional Edge: Seeking Hidden Risks Using Regular Variation (2011, methodology): “The mathematical framework of multivariate regular variation provides tools to compute tail probabilities associated with such risks; see [3], [11], and [21, Chapter 6].”