Max-stable processes are a popular tool for the study of environmental extremes, and the extremal skew-t process is a general model that allows for a flexible extremal dependence structure. For inference on max-stable processes with high-dimensional data, exact likelihood-based estimation is computationally intractable. Composite likelihoods, using lower dimensional components, and Stephenson-Tawn likelihoods, using occurrence times of maxima, are both attractive methods to circumvent this issue for moderate dimensions. In this article we establish the theoretical formulae for simulations of and inference for the extremal skew-t process. We also incorporate the Stephenson-Tawn concept into the composite likelihood framework, giving greater statistical and computational efficiency for higher-order composite likelihoods. We compare 2-way (pairwise), 3-way (triplewise), 4-way, 5-way and 10-way composite likelihoods for models of up to 100 dimensions. Furthermore, we propose cdf approximations for the Stephenson-Tawn likelihood function, leading to large computational gains, and enabling accurate fitting of models in large dimensions in only a few minutes. We illustrate our methodology with an application to a 90-dimensional temperature dataset from Melbourne, Australia.

最大稳定方法可用于极端环境的研究的流行工具，和极值skew-吨处理是一般的模型，它允许一个灵活的极值相关结构。为了推断具有高维数据的最大稳定过程，基于精确的似然估计在计算上是棘手的。使用较低维分量的合成似然率和使用最大值出现时间的Stephenson-Tawn似然率都是在中等维数下规避此问题的有吸引力的方法。在本文中，我们建立了理论公式的模拟和推理的极值skew- ŧ处理。我们还将Stephenson-Tawn概念整合到复合似然框架中，从而为更高阶的复合似然提供了更高的统计和计算效率。对于最多100个维度的模型，我们比较2向（成对），3向（三向），4向，5向和10向复合可能性。此外，我们提出了Stephenson-Tawn似然函数的cdf近似值，从而带来了较大的计算量，并且仅需几分钟即可对大型模型进行精确拟合。我们将其应用到来自澳大利亚墨尔本的90维温度数据集中来说明我们的方法。