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    Rights statement: 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

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Properties of extremal dependence models built on bivariate max-linearity

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Properties of extremal dependence models built on bivariate max-linearity. / Kereszturi, Mónika; Tawn, Jonathan.

In: Journal of Multivariate Analysis, Vol. 155, 03.2017, p. 52-71.

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@article{2f4b737f99774a56b485a3fe1ed39410,
title = "Properties of extremal dependence models built on bivariate max-linearity",
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.",
keywords = "Bivariate extremes, Max-linear models, Extremal dependence, Asymptotic independence",
author = "M{\'o}nika Kereszturi and Jonathan Tawn",
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",
year = "2017",
month = "3",
doi = "10.1016/j.jmva.2016.12.001",
language = "English",
volume = "155",
pages = "52--71",
journal = "Journal of Multivariate Analysis",
issn = "0047-259X",
publisher = "Academic Press Inc.",

}

RIS

TY - JOUR

T1 - Properties of extremal dependence models built on bivariate max-linearity

AU - Kereszturi, Mónika

AU - Tawn, Jonathan

N1 - 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

PY - 2017/3

Y1 - 2017/3

N2 - 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.

AB - 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.

KW - Bivariate extremes

KW - Max-linear models

KW - Extremal dependence

KW - Asymptotic independence

U2 - 10.1016/j.jmva.2016.12.001

DO - 10.1016/j.jmva.2016.12.001

M3 - Journal article

VL - 155

SP - 52

EP - 71

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

SN - 0047-259X

ER -