A new class of models for bivariate joint tails

Alexandra Ramos and Anthony Ledford

Journal Of The Royal Statistical Society Series B, 2009, vol. 71, issue 1, pages 219-241

Abstract: A fundamental issue in applied multivariate extreme value analysis is modelling dependence within joint tail regions. The primary focus of this work is to extend the classical pseudopolar treatment of multivariate extremes to develop an asymptotically motivated representation of extremal dependence that also encompasses asymptotic independence. Starting with the usual mild bivariate regular variation assumptions that underpin the coefficient of tail dependence as a measure of extremal dependence, our main result is a characterization of the limiting structure of the joint survivor function in terms of an essentially arbitrary non-negative measure that must satisfy some mild constraints. We then construct parametric models from this new class and study in detail one example that accommodates asymptotic dependence, asymptotic independence and asymmetry within a straightforward parsimonious parameterization. We provide a fast simulation algorithm for this example and detail likelihood-based inference including tests for asymptotic dependence and symmetry which are useful for submodel selection. We illustrate this model by application to both simulated and real data. In contrast with the classical multivariate extreme value approach, which concentrates on the limiting distribution of normalized componentwise maxima, our framework focuses directly on the structure of the limiting joint survivor function and provides significant extensions of both the theoretical and the practical tools that are available for joint tail modelling. Copyright (c) 2009 Royal Statistical Society.

Date: 2009

Downloads: (external link)
http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9868.2008.00684.x link to full text (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: http://EconPapers.repec.org/RePEc:bla:jorssb:v:71:y:2009:i:1:p:219-241

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=1369-7412

Access Statistics for this article

Journal Of The Royal Statistical Society Series B is edited by C. Robert and A. T. A. Wood

More articles in Journal Of The Royal Statistical Society Series B from Royal Statistical Society
Series data maintained by Christopher F. Baum ().