It is no secret that statistical modelling often involves making simplifying assumptions when attempting to study complex stochastic phenomena. Spatial modelling of extreme values is no exception, with one of the most common such assumptions being stationarity in the marginal and/or dependence features. If non-stationarity has been detected in the marginal distributions, it is tempting to try to model this while assuming stationarity in the dependence, without necessarily putting this latter assumption through thorough testing. However, margins and dependence are often intricately connected and the detection of non-stationarity in one feature might affect the detection of non-stationarity in the other. This work is an in-depth case study of this interrelationship, with a particular focus on a spatio-temporal environmental application exhibiting well-documented marginal non-stationarity. Specifically, we compare and contrast four different marginal detrending approaches in terms of our post-detrending ability to detect temporal non-stationarity in the spatial extremal dependence structure of a sea surface temperature dataset from the Red Sea.

翻译：统计建模在研究复杂随机现象时常需引入简化假设，这已是公开的秘密。空间极值建模亦不例外，其中最普遍的假设之一是边缘分布和/或相依特征的平稳性。若在边缘分布中检测到非平稳性，研究者往往倾向于在假设相依结构平稳的前提下仅对边缘特征建模，却未必对后一假设进行充分检验。然而，边缘特征与相依结构常存在错综复杂的关联，某一特征的非平稳性检测结果可能影响另一特征的非平稳性判定。本研究通过一个具有充分文献记载的边缘非平稳性的时空环境应用案例，对此交互关系展开深入探讨。具体而言，我们以红海海表温度数据集为对象，比较了四种不同的边缘去趋势方法，重点评估经去趋势处理后对空间极值相依结构中时间非平稳性的检测能力。