Properties of extremal dependence models built on bivariate max-linearity

Kereszturi, Mónika and Tawn, Jonathan (2017) Properties of extremal dependence models built on bivariate max-linearity. Journal of Multivariate Analysis, 155. pp. 52-71. ISSN 0047-259X

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Bivariate max-linear models provide a core building block for characterizing bivariate max-stable distributions. The limiting distribution of marginally normalized component-wise maxima of bivariate max-linear models can be dependent (asymptotically dependent) or independent (asymptotically independent). However, for modeling bivariate extremes they have weaknesses in that they are exactly max-stable with no penultimate form of convergence to asymptotic dependence, and asymptotic independence arises if and only if the bivariate max-linear model is independent. In this work we present more realistic structures for describing bivariate extremes. We show that these models are built on bivariate max-linearity but are much more general. In particular, we present models that are dependent but asymptotically independent and others that are asymptotically dependent but have penultimate forms. We characterize the limiting behavior of these models using two new different angular measures in a radial-angular representation that reveal more structure than existing measures.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Multivariate Analysis
Additional Information:
This is the author’s version of a work that was accepted for publication in Journal of Multivariate Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Multivariate Analysis, 155, 2017 DOI: 10.1016/j.jmva.2016.12.001
Uncontrolled Keywords:
?? bivariate extremesmax-linear modelsextremal dependenceasymptotic independencestatistics and probabilitystatistics, probability and uncertaintynumerical analysis ??
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Deposited On:
13 Dec 2016 11:30
Last Modified:
11 Nov 2023 00:19