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.

中文翻译：

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新条件多元极端模型的亚渐近动机

极值的统计模型通常源自非退化概率极限，可用于近似超过选定高阈值的事件分布。如果收敛到极限分布很慢，那么近似值可能无法很好地描述观察到的极端情况，并且只能通过选择一个非常高的阈值来减少偏差，代价是在任何后续的尾部推断中都会出现不可接受的大方差。另一种方法是使用亚渐近极值模型，该模型引入了更多参数，但可以为较低的阈值提供更好的拟合。我们在适用于多元极端的 Heffernan-Tawn 条件尾模型的背景下考虑这个问题，由于其在高维应用中灵活处理依赖关系，该模型已被广泛使用。该模型的最新扩展似乎改进了联合尾部推理。我们寻求亚渐近证明为什么这些扩展有效，并表明它们可以将某些 copula 的收敛速度提高一个数量级。我们还提出了它们的一类扩展，它们可能对多元极端情况下的统计推断具有更广泛的价值。