In this paper, we introduce a new class of models for spatial data obtained from max-convolution processes based on indicator kernels with random shape. We show that this class of models have appealing dependence properties including tail dependence at short distances and independence at long distances. We further consider max-convolutions between such processes and processes with tail independence, in order to separately control the bulk and tail dependence behaviors, and to increase flexibility of the model at longer distances, in particular, to capture intermediate tail dependence. We show how parameters can be estimated using a weighted pairwise likelihood approach, and we conduct an extensive simulation study to show that the proposed inference approach is feasible in high dimensions and it yields accurate parameter estimates in most cases. We apply the proposed methodology to analyse daily temperature maxima measured at 100 monitoring stations in the state of Oklahoma, US. Our results indicate that our proposed model provides a good fit to the data, and that it captures both the bulk and the tail dependence structures accurately.

翻译：本文提出了一类新的空间数据模型，该模型基于具有随机形状的指示核的最大卷积过程。我们证明这类模型具有良好的依赖性质，包括短距离上的尾部依赖和长距离上的独立性。为进一步分别控制主体与尾部依赖行为、增强模型在较长距离上的灵活性（特别是捕捉中等尾部依赖），我们进一步考虑了此类过程与具有尾部独立性的过程之间的最大卷积。我们展示了如何利用加权成对似然方法估计参数，并通过大规模模拟研究表明所提出的推断方法在高维场景下可行，且在多数情况下能获得准确的参数估计。我们将所提方法应用于分析美国俄克拉荷马州100个监测站测得的每日最高温度数据，结果表明我们的模型能够良好拟合数据，并准确捕捉主体与尾部依赖结构。