Conditional extreme value models: fallacies and pitfalls

Conditional extreme value models have been introduced by Heffernan and Resnick (Ann. Appl. Probab., 17 , 537–571, 2007 ) to describe the asymptotic behavior of a random vector as one specific component becomes extreme. Obviously, this class of models is related to classical multivariate extreme valu...

Full description

Saved in:
Bibliographic Details
Published in:Extremes (Boston) 2017-12, Vol.20 (4), p.777-805
Main Authors: Drees, Holger, Janßen, Anja
Format: Article
Language:English
Subjects:
Asymptotic properties
Civil Engineering
Economics
Environmental Management
Extreme value theory
Extreme values
Finance
Hydrogeology
Insurance
Management
Mathematics and Statistics
Normal distribution
Quality Control
Reliability
Safety and Risk
Standardization
Statistics
Statistics for Business
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Conditional extreme value models have been introduced by Heffernan and Resnick (Ann. Appl. Probab., 17 , 537–571, 2007 ) to describe the asymptotic behavior of a random vector as one specific component becomes extreme. Obviously, this class of models is related to classical multivariate extreme value theory which describes the behavior of a random vector as its norm (and therefore at least one of its components) becomes extreme. However, it turns out that this relationship is rather subtle and sometimes contrary to intuition. We clarify the differences between the two approaches with the help of several illuminative (counter)examples. Furthermore, we discuss marginal standardization, which is a useful tool in classical multivariate extreme value theory but, as we point out, much less straightforward and sometimes even obscuring in conditional extreme value models. Finally, we indicate how, in some situations, a more comprehensive characterization of the asymptotic behavior can be obtained if the conditions of conditional extreme value models are relaxed so that the limit is no longer unique.
ISSN:1386-1999
1572-915X
DOI:10.1007/s10687-017-0293-5