Rights statement: https://www.cambridge.org/core/journals/advances-in-applied-probability/article/linking-representations-for-multivariate-extremes-via-a-limit-set/9A77F8E10602DC13EA26E429CFB5FD21 The final, definitive version of this article has been published in the Journal, Advances in Applied Probability, 54 (3), pp 688-717 2022, © 2022 Cambridge University Press.
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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Linking representations for multivariate extremes via a limit set
AU - Nolde, Natalia
AU - Wadsworth, Jennifer
N1 - https://www.cambridge.org/core/journals/advances-in-applied-probability/article/linking-representations-for-multivariate-extremes-via-a-limit-set/9A77F8E10602DC13EA26E429CFB5FD21 The final, definitive version of this article has been published in the Journal, Advances in Applied Probability, 54 (3), pp 688-717 2022, © 2022 Cambridge University Press.
PY - 2022/9/30
Y1 - 2022/9/30
N2 - The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously large. Various alternative dependence measures and representations have been proposed, with the most well-known being hidden regular variation and the conditional extreme value model. These varying depictions of extremal dependence arise through consideration of different parts of the multivariate domain, and particularly exploring what happens when extremes of one variable may grow at different rates to other variables. Thus far, these alternative representations have come from distinct sources and links between them are limited. In this work we elucidate many of the relevant connections through a geometrical approach. In particular, the shape of the limit set of scaled sample clouds in light-tailed margins is shown to provide a description of several different extremal dependence representations.
AB - The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously large. Various alternative dependence measures and representations have been proposed, with the most well-known being hidden regular variation and the conditional extreme value model. These varying depictions of extremal dependence arise through consideration of different parts of the multivariate domain, and particularly exploring what happens when extremes of one variable may grow at different rates to other variables. Thus far, these alternative representations have come from distinct sources and links between them are limited. In this work we elucidate many of the relevant connections through a geometrical approach. In particular, the shape of the limit set of scaled sample clouds in light-tailed margins is shown to provide a description of several different extremal dependence representations.
KW - Multivariate extreme value theory
KW - conditional extremes
KW - hidden regular variation
KW - limit set
KW - asymptotic (in)dependence
M3 - Journal article
VL - 54
SP - 688
EP - 717
JO - Advances in Applied Probability
JF - Advances in Applied Probability
SN - 0001-8678
IS - 3
ER -