We study the class of dependence models for spatial data obtained from Cauchy convolution processes based on different types of kernel functions. We show that the resulting spatial processes have appealing tail dependence properties, such as tail dependence at short distances and independence at long distances with suitable kernel functions. We derive the extreme-value limits of these processes, study their smoothness properties, and detail some interesting special cases. To get higher flexibility at sub-asymptotic levels and separately control the bulk and the tail dependence properties, we further propose spatial models constructed by mixing a Cauchy convolution process with a Gaussian process. We demonstrate that this framework indeed provides a rich class of models for the joint modelling of the bulk and the tail behaviors. Our proposed inference approach relies on matching model-based and empirical summary statistics, and an extensive simulation study shows that it yields accurate estimates. We demonstrate our new methodology by application to a temperature dataset measured at 97 monitoring stations in the state of Oklahoma, US. Our results indicate that our proposed model provides a very good fit to the data, and that it captures both the bulk and the tail dependence structures accurately.
翻译:我们根据不同类型的内核功能,对从卷土重来过程中获得的空间数据依赖模型的类别进行研究,我们发现,由此形成的空间过程具有吸引尾部依赖特性,例如短距离尾部依赖和长距离独立,具有适当的内核功能;我们从这些过程的极端价值限度中得出这些过程的顺利性,研究其顺利性,并细化一些有趣的特殊案例;为了在次防波层获得更大的灵活性,并单独控制散装和尾部依赖特性,我们进一步提出空间模型,通过将卷土重来与高斯进程混合来构建这些空间模型;我们证明,这一框架确实为联合模拟散装和尾部行为提供了丰富的模型。我们提议的推断方法依赖于基于模型的匹配和实证的汇总统计数据,以及广泛的模拟研究表明,它得出准确的估计数。我们通过应用美国俄克拉何马州97个监测站测量的温度数据集来展示我们的新方法。我们提出的模型表明,我们提议的模型非常适合数据,并且准确地捕捉散装和尾部依赖结构。