For many environmental processes, recent studies have shown that the dependence strength is decreasing when quantile levels increase. This implies that the popular max-stable models are inadequate to capture the rate of joint tail decay, and to estimate joint extremal probabilities beyond observed levels. We here develop a more flexible modeling framework based on the class of max-infinitely divisible processes, which extend max-stable processes while retaining dependence properties that are natural for maxima. We propose two parametric constructions for max-infinitely divisible models, which relax the max-stability property but remain close to some popular max-stable models obtained as special cases. The first model considers maxima over a finite, random number of independent observations, while the second model generalizes the spectral representation of max-stable processes. Inference is performed using a pairwise likelihood. We illustrate the benefits of our new modeling framework on Dutch wind gust maxima calculated over different time units. Results strongly suggest that our proposed models outperform other natural models, such as the Student-t copula process and its max-stable limit, even for large block sizes.

中文翻译：

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空间极值的最大无限可分模型和推理

对于许多环境过程，最近的研究表明，当分位数水平增加时，依赖性强度会降低。这意味着流行的最大稳定模型不足以捕捉联合尾部衰减的速率，也不足以估计超出观察水平的联合极值概率。我们在这里开发了一个基于最大无限可分过程类的更灵活的建模框架，该框架扩展了最大稳定过程，同时保留了最大值的自然依赖性。我们为最大无限可分模型提出了两种参数构造，它们放宽了最大稳定性属性，但仍然接近作为特殊情况获得的一些流行的最大稳定模型。第一个模型在有限的、随机数量的独立观测值上考虑最大值，而第二个模型概括了最大稳定过程的谱表示。使用成对似然进行推理。我们说明了我们的新建模框架对在不同时间单位计算的荷兰阵风最大值的好处。结果强烈表明，我们提出的模型优于其他自然模型，例如 Student-t copula 过程及其最大稳定限制，即使对于大块大小也是如此。