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Properties of extremal dependence models built on bivariate max-linearity

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>03/2017
<mark>Journal</mark>Journal of Multivariate Analysis
Volume155
Number of pages20
Pages (from-to)52-71
<mark>State</mark>Published
Early online date9/12/16
<mark>Original language</mark>English

Abstract

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.

Bibliographic note

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