B0508
Title: Conditional extreme value models: Fallacies and pitfalls
Authors: Holger Drees - University of Hamburg (Germany) [presenting]
Anja Janssen - University of Copenhagen (Denmark)
Abstract: Classical multivariate extreme value theory deals with the behavior of random vectors when at least one component is large. Sometimes, however, one is interested in the behavior of the vector when not an arbitrary, but a pre-specified component is large. To this end, the so-called conditional extreme value (CEV) models were introduced and their relation to classical multivariate extreme value models was discussed. We first recall concepts of marginal standardization in CEV models from the literature. We will illustrate by counterexamples that the standardization of the not necessarily extreme components is not well adapted to the particular features of the CEV models. From the above interpretation, it seems plausible that (under mild extra conditions ruling out degenerate cases) the classical multivariate extreme value model for a random vector implies that the assumptions of all CEV models which suppose that one specific component is large are fulfilled, and vice versa. Unfortunately, the precise relationship between the CEV models and the classical multivariate extreme value model turns out to be much more intricate than intuition suggests. In particular, we give counterexamples to several claims about this relation which can be found in the literature. Time permitting, we finally discuss alternative modeling approaches which avoid some of the drawbacks of CEV models, but exhibit other shortcomings.
Journal