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

Lugrin, Thomas and Tawn, Jonathan and Davison, Anthony (2021) Sub-asymptotic results to motivate a new conditional multivariate extremes model. Stat. ISSN 2049-1573 (In Press)

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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.

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27 Aug 2021 10:25
In Press
Last Modified:
19 Nov 2021 11:54