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  • LugrinTawnDavison

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Sub-asymptotic results to motivate a new conditional multivariate extremes model.

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<mark>Journal publication date</mark>27/06/2021
<mark>Journal</mark>Stat
Publication StatusAccepted/In press
<mark>Original language</mark>English

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.