Abstract
In classical extreme value theory probabilities of extreme events are estimated assuming all the components of a random vector to be in a domain of attraction of an extreme value distribution. In contrast, the conditional extreme value model assumes a domain of attraction condition on a sub-collection of the components of a multivariate random vector. This model has been studied in Heffernan and Tawn (JRSS B 66(3):497–546, 2004), Heffernan and Resnick (Ann Appl Probab 17(2):537–571, 2007), and Das and Resnick (2009). In this paper we propose three statistics which act as tools to detect this model in a bivariate set-up. In addition, the proposed statistics also help to distinguish between two forms of the limit measure that is obtained in the model.
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B. Das and S. Resnick were partially supported by ARO Contract W911NF-07-1-0078 at Cornell University.
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Das, B., Resnick, S.I. Detecting a conditional extreme value model. Extremes 14, 29–61 (2011). https://doi.org/10.1007/s10687-009-0097-3
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DOI: https://doi.org/10.1007/s10687-009-0097-3
Keywords
- Regular variation
- Domain of attraction
- Heavy tails
- Asymptotic independence
- Conditional extreme value model