Rights statement: This is the peer reviewed version of the following article: Thomas Lugrin, Jonathan A. Tawn, Anthony C. Davison (2021), Sub-asymptotic motivation for new conditional multivariate extreme models. Journal of Stat. doi: 10.1002/sta4.401 which has been published in final form at https://onlinelibrary.wiley.com/doi/10.1002/sta4.401 This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.
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Final published version
Licence: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Sub-asymptotic motivation for new conditional multivariate extreme models
AU - Lugrin, Thomas
AU - Tawn, Jonathan
AU - Davison, Anthony
N1 - This is the peer reviewed version of the following article: Thomas Lugrin, Jonathan A. Tawn, Anthony C. Davison (2021), Sub-asymptotic motivation for new conditional multivariate extreme models. Journal of Stat. doi: 10.1002/sta4.401 which has been published in final form at https://onlinelibrary.wiley.com/doi/10.1002/sta4.401 This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.
PY - 2021/12/31
Y1 - 2021/12/31
N2 - Statistical models for extreme values are generally derived from non-degenerate probabilistic limits that can be used to approximate the distribution of events that exceed a selected high threshold. If convergence to the limit distribution is slow, then the approximation may describe observed extremes poorly, and bias can only be reduced by choosing a very high threshold at the cost of unacceptably large variance in any subsequent tail inference. An alternative is to use sub-asymptotic extremal models, which introduce more parameters but can provide better fits for lower thresholds. We consider this problem in the context of the Heffernan–Tawn conditional tail model for multivariate extremes, which has found wide use due to its flexible handling of dependence in high-dimensional applications. Recent extensions of this model appear to improve joint tail inference. We seek a sub-asymptotic justification for why these extensions work and show that they can improve convergence rates by an order of magnitude for certain copulas. We also propose a class of extensions of them that may have wider value for statistical inference in multivariate extremes.
AB - Statistical models for extreme values are generally derived from non-degenerate probabilistic limits that can be used to approximate the distribution of events that exceed a selected high threshold. If convergence to the limit distribution is slow, then the approximation may describe observed extremes poorly, and bias can only be reduced by choosing a very high threshold at the cost of unacceptably large variance in any subsequent tail inference. An alternative is to use sub-asymptotic extremal models, which introduce more parameters but can provide better fits for lower thresholds. We consider this problem in the context of the Heffernan–Tawn conditional tail model for multivariate extremes, which has found wide use due to its flexible handling of dependence in high-dimensional applications. Recent extensions of this model appear to improve joint tail inference. We seek a sub-asymptotic justification for why these extensions work and show that they can improve convergence rates by an order of magnitude for certain copulas. We also propose a class of extensions of them that may have wider value for statistical inference in multivariate extremes.
KW - asymptotic dependence
KW - asymptotic independence
KW - conditional extremes
KW - Gaussian distribution
KW - logistic model
KW - sub-asymptotic approximation
U2 - 10.1002/sta4.401
DO - 10.1002/sta4.401
M3 - Journal article
VL - 10
JO - Stat
JF - Stat
SN - 2049-1573
IS - 1
M1 - e401
ER -