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A new representation for multivariate tail probabilities

Wadsworth, Jennifer and Tawn, Jon (2013) A new representation for multivariate tail probabilities. Bernoulli, 19 (5B). pp. 2689-2714. ISSN 1350-7265

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Abstract

Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components of a random vector, standardized to identical margins, grow at the same rate. In this paper, we consider the effect of allowing the components to grow at different rates, and characterize the link between these marginal growth rates and the multivariate tail probability decay rate. Our approach leads to a whole class of univariate regular variation conditions, in place of the single but multivariate regular variation conditions that underpin the current theories. These conditions are indexed by a homogeneous function and an angular dependence function, which, for asymptotically independent random vectors, mirror the role played by the exponent measure and Pickands’ dependence function in classical multivariate extremes. We additionally offer an inferential approach to joint survivor probability estimation. The key feature of our methodology is that extreme set probabilities can be estimated by extrapolating upon rays emanating from the origin when the margins of the variables are exponential. This offers an appreciable improvement over existing techniques where extrapolation in exponential margins is upon lines parallel to the diagonal.

Item Type: Article
Journal or Publication Title: Bernoulli
Uncontrolled Keywords: asymptotic independence ; coefficient of tail dependence ; multivariate extreme value theory ; Pickands’ dependence function ; regular variation
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 54871
Deposited By: ep_importer_pure
Deposited On: 06 Jun 2012 10:54
Refereed?: Yes
Published?: Published
Last Modified: 04 Dec 2013 09:52
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/54871

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