Motivated by the widespread use of large gridded data sets in the atmospheric sciences, we propose a new model for extremes of areal data that is inspired by the simultaneous autoregressive (SAR) model in classical spatial statistics. Our extreme SAR model extends recent work on transformed‐linear operations applied to regularly varying random vectors, and is unique among extremes models in being directly analogous to a classical linear model. An additional appeal is its simplicity; given a proximity matrix W, spatial dependence is described by a single parameter $\rho$. We develop an estimation method that minimizes the discrepancy between the tail pairwise dependence matrix (TPDM) for the fitted model and the estimated TPDM. Applying this method to simulated data demonstrates that it is able to produce good estimates of extremal spatial dependence even in the case of model misspecification, and additionally produces reasonable estimates of uncertainty. We also apply the method to gridded precipitation observations for a study region over northeast Colorado, and find that a single‐parameter extreme SAR model paired with a neighborhood structure which accounts for longer range dependence effectively models spatial dependence in these data.

中文翻译：

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空间极限的同时自回归模型

受大气科学中大网格数据集的广泛使用的启发，我们提出了一种针对面积数据极端值的新模型，该模型受经典空间统计中的同时自回归（SAR）模型的启发。我们的极限SAR模型扩展了最近对应用于规则变化的随机矢量的变换线性运算的工作，并且在极限模型中与常规线性模型直接相似，因此是独一无二的。另一个吸引力是它的简单性；给定一个接近矩阵W，空间相关性由单个参数描述$\rho$。我们开发了一种估计方法，该方法可使拟合模型的尾部成对依赖矩阵（TPDM）与估计的TPDM之间的差异最小化。将这种方法应用于模拟数据表明，即使在模型错误指定的情况下，它也能够产生极好的空间依赖性估计，并且还能产生不确定性的合理估计。我们还将这种方法应用于科罗拉多州东北部某研究区域的网格降水观测中，发现单参数极端SAR模型与邻域结构配对，该邻域结构解释了较长的距离依赖性，可以有效地模拟这些数据中的空间依赖性。