Flexible and fast spatial return level estimation via a spatially-fused penalty

Spatial extremes are common for climate data as the observations are usually referenced by geographic locations and dependent when they are nearby. An important goal of extremes modeling is to estimate the <i>T</i>-year return level. Among the methods suitable for modeling spatial extremes, perhaps the simplest and fastest approach is the spatial generalized extreme value (GEV) distribution and the spatial generalized Pareto distribution (GPD) that assume marginal independence and only account for dependence through the parameters. Despite the simplicity, simulations have shown that return level estimation using the spatial GEV and spatial GPD still provides satisfactory results compared to max-stable processes, which are asymptotically justified models capable of representing spatial dependence among extremes. However, the linear functions used to model the spatially varying coefficients are restrictive and may be violated. We propose a flexible and fast approach based on the spatial GEV and spatial GPD by introducing fused lasso and fused ridge penalty for parameter regularization. This enables improved return level estimation for large spatial extremes compared to the existing methods.

气候数据中的空间极值现象极为普遍，这是因为观测值均以地理位置进行标注，且邻近位置的观测之间存在相关性。极值建模的一项核心目标是估算<i>T</i>年重现水平。在适用于空间极值建模的各类方法中，最为简便快捷的当属空间广义极值（GEV）分布与空间广义帕累托（GPD）分布，这类模型假设边缘独立，仅通过参数项刻画空间相关性。尽管这类方法十分简洁，但仿真实验表明，相较于最大稳定过程——一类能够刻画极值间空间相关性且具备渐近理论支撑的模型——采用空间GEV与空间GPD进行重现水平估算，仍可获得令人满意的结果。然而，这类方法中用于建模空间变系数的线性函数存在较强的限制性，在实际应用中往往难以契合真实数据的分布规律。为此，我们提出一种基于空间GEV与空间GPD的灵活高效建模方法，通过引入融合套索（fused lasso）与融合岭惩罚项（fused ridge penalty）实现参数正则化。相较于现有方法，该方法可大幅提升大规模空间极值场景下的重现水平估算精度。