Abstract

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 T-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. Supplemental files for this article are available online.

摘要

空间极端值对于气候数据来说很常见，因为观测结果通常由地理位置引用，并且取决于它们何时位于附近。极端建模的一个重要目标是估计 T 年回报水平。在适用于空间极值建模的方法中，也许最简单和最快的方法是空间广义极值 (GEV) 分布和空间广义帕累托分布 (GPD)，它们假设边际独立并且仅通过参数考虑相关性。尽管简单，但模拟表明，与最大稳定过程相比，使用空间 GEV 和空间 GPD 的回报水平估计仍然提供令人满意的结果，最大稳定过程是能够表示极端之间空间依赖性的渐近证明模型。然而，用于对空间变化系数建模的线性函数具有限制性，可能会被违反。我们提出了一种基于空间 GEV 和空间 GPD 的灵活快速的方法，通过引入融合 lasso 和融合岭惩罚来进行参数正则化。与现有方法相比，这可以改进对大空间极端值的回报水平估计。本文的补充文件可在线获取。