Statistical modeling of a nonstationary spatial extremal dependence structure is challenging. Max-stable processes are common choices for modeling spatially-indexed block maxima, where an assumption of stationarity is usual to make inference feasible. However, this assumption is often unrealistic for data observed over a large or complex domain. We propose a computationally-efficient method for estimating extremal dependence using a globally nonstationary, but locally-stationary, max-stable process by exploiting nonstationary kernel convolutions. We divide the spatial domain into a fine grid of subregions, assign each of them its own dependence parameters, and use LASSO ($L_1$) or ridge ($L_2$) penalties to obtain spatially-smooth parameter estimates. We then develop a novel data-driven algorithm to merge homogeneous neighboring subregions. The algorithm facilitates model parsimony and interpretability. To make our model suitable for high-dimensional data, we exploit a pairwise likelihood to draw inferences and discuss computational and statistical efficiency. An extensive simulation study demonstrates the superior performance of our proposed model and the subregion-merging algorithm over the approaches that either do not model nonstationarity or do not update the domain partition. We apply our proposed method to model monthly maximum temperatures at over 1400 sites in Nepal and the surrounding Himalayan and sub-Himalayan regions; we again observe significant improvements in model fit compared to a stationary process and a nonstationary process without subregion-merging. Furthermore, we demonstrate that the estimated merged partition is interpretable from a geographic perspective and leads to better model diagnostics by adequately reducing the number of subregion-specific parameters.

翻译：对非平稳空间极端依赖结构进行统计建模极具挑战性。最大稳定过程是建模空间索引块最大值的常用选择，其中通常假设平稳性以简化推断。然而，这一假设对于在广阔或复杂区域上观测到的数据往往不切实际。我们提出一种计算高效的方法，通过利用非平稳核卷积来估计基于全局非平稳但局部平稳的最大稳定过程的极端依赖性。将空间域划分为精细子区域网格，为每个子区域分配独立的依赖参数，并使用LASSO（$L_1$）或岭回归（$L_2$）惩罚获得空间平滑的参数估计。随后开发一种新颖的数据驱动算法，合并同质的相邻子区域，该算法有助于实现模型简约性与可解释性。为使模型适用于高维数据，我们利用成对似然进行推断，并讨论计算与统计效率。广泛的仿真研究表明，所提出的模型和子区域合并算法相比不建模非平稳性或未更新域划分的方法具有更优性能。我们将所提方法应用于尼泊尔及周边喜马拉雅与次喜马拉雅地区1400余个站点的月最高温度建模，再次观察到较平稳过程及无子区域合并的非平稳过程在模型拟合上的显著改进。此外，合并后的分区估计具有地理可解释性，并通过充分减少子区域特定参数数量提升了模型诊断效果。