Detecting a Conditional Extreme Value Model
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
\cite{heffernan:tawn:2004,heffernan:resnick:2007,das:resnick:2008a}.
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.