Sub-asymptotic motivation for new conditional multivariate extreme models

Lugrin, Thomas and Tawn, Jonathan and Davison, Anthony (2021) Sub-asymptotic motivation for new conditional multivariate extreme models. Stat, 10 (1). ISSN 2049-1573

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Abstract

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.

Item Type:
Journal Article
Journal or Publication Title:
Stat
Additional Information:
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.
Subjects:
ID Code:
158939
Deposited By:
Deposited On:
27 Aug 2021 10:25
Refereed?:
Yes
Published?:
Published
Last Modified:
27 Jun 2022 23:35