Modeling the extremal dependence structure of spatial data is considerably easier if that structure is stationary. However, for data observed over large or complicated domains, nonstationarity will often prevail. Current methods for modeling nonstationarity in extremal dependence rely on models that are either computationally difficult to fit or require prior knowledge of covariates. Sampson and Guttorp (1992) proposed a simple technique for handling nonstationarity in spatial dependence by smoothly mapping the sampling locations of the process from the original geographical space to a latent space where stationarity can be reasonably assumed. We present an extension of this method to a spatial extremes framework by considering least squares minimization of pairwise theoretical and empirical extremal dependence measures. Along with some practical advice on applying these deformations, we provide a detailed simulation study in which we propose three spatial processes with varying degrees of nonstationarity in their extremal and central dependence structures. The methodology is applied to Australian summer temperature extremes and UK precipitation to illustrate its efficacy compared with a naive modeling approach.

中文翻译：

---

非平稳极值依赖的空间变形

如果该结构是固定的，则对空间数据的极值依赖结构进行建模要容易得多。然而，对于在大型或复杂域上观察到的数据，非平稳性通常会占上风。当前用于对极值依赖性中的非平稳性进行建模的方法依赖于在计算上难以拟合或需要协变量先验知识的模型。Sampson 和 Guttorp (1992) 提出了一种处理空间依赖性非平稳性的简单技术，方法是将过程的采样位置从原始地理空间平滑地映射到可以合理假设平稳性的潜在空间。我们通过考虑成对理论和经验极值依赖度量的最小二乘最小化，将此方法扩展到空间极值框架。除了关于应用这些变形的一些实用建议外，我们还提供了详细的模拟研究，其中我们提出了三个空间过程，它们的极值和中心依赖结构具有不同程度的非平稳性。该方法应用于澳大利亚夏季极端温度和英国降水，以说明与简单建模方法相比的有效性。