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Modelling across extremal dependence classes
Author(s) -
Wadsworth J. L.,
Tawn J. A.,
Davison A. C.,
Elton D. M.
Publication year - 2017
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12157
Subject(s) - bivariate analysis , extrapolation , variety (cybernetics) , representation (politics) , inference , class (philosophy) , range (aeronautics) , simple (philosophy) , model selection , limit (mathematics) , mathematics , selection (genetic algorithm) , parametric statistics , econometrics , variable (mathematics) , computer science , statistical physics , statistics , artificial intelligence , mathematical analysis , philosophy , materials science , physics , epistemology , politics , political science , law , composite material
Summary Different dependence scenarios can arise in multivariate extremes, entailing careful selection of an appropriate class of models. In bivariate extremes, the variables are either asymptotically dependent or are asymptotically independent. Most available statistical models suit one or other of these cases, but not both, resulting in a stage in the inference that is unaccounted for but can substantially impact subsequent extrapolation. Existing modelling solutions to this problem are either applicable only on subdomains or appeal to multiple limit theories. We introduce a unified representation for bivariate extremes that encompasses a wide variety of dependence scenarios and applies when at least one variable is large. Our representation motivates a parametric model that encompasses both dependence classes. We implement a simple version of this model and show that it performs well in a range of settings.