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A conditional approach to modelling multivariate extreme values (with discussion).

Research output: Contribution to journalJournal article

Published

Journal publication date08/2004
JournalJournal of the Royal Statistical Society Series B (Statistical Methodology)
Journal number3
Volume66
Number of pages51
Pages497-547
Original languageEnglish

Abstract

Summary. Multivariate extreme value theory and methods concern the characterization, estimation and extrapolation of the joint tail of the distribution of a d-dimensional random variable. Existing approaches are based on limiting arguments in which all components of the variable become large at the same rate. This limit approach is inappropriate when the extreme values of all the variables are unlikely to occur together or when interest is in regions of the support of the joint distribution where only a subset of components is extreme. In practice this restricts existing methods to applications where d is typically 2 or 3. Under an assumption about the asymptotic form of the joint distribution of a d-dimensional random variable conditional on its having an extreme component, we develop an entirely new semiparametric approach which overcomes these existing restrictions and can be applied to problems of any dimension. We demonstrate the performance of our approach and its advantages over existing methods by using theoretical examples and simulation studies. The approach is used to analyse air pollution data and reveals complex extremal dependence behaviour that is consistent with scientific understanding of the process. We find that the dependence structure exhibits marked seasonality, with ex- tremal dependence between some pollutants being significantly greater than the dependence at non-extreme levels.

Bibliographic note

RAE_import_type : Journal article RAE_uoa_type : Statistics and Operational Research