Max-infinitely divisible (max-id) processes play a central role in extreme-value theory and include the subclass of all max-stable processes. They allow for a constructive representation based on the componentwise maximum of random functions drawn from a Poisson point process defined on a suitable functions space. Simulating from a max-id process is often difficult due to its complex stochastic structure, while calculating its joint density in high dimensions is often numerically infeasible. Therefore, exact and efficient simulation techniques for max-id processes are useful tools for studying the characteristics of the process and for drawing statistical inferences. Inspired by the simulation algorithms for max-stable processes, we here develop theory and algorithms to generalize simulation approaches tailored for certain flexible (existing or new) classes of max-id processes. Efficient simulation for a large class of models can be achieved by implementing an adaptive rejection sampling scheme to sidestep a numerical integration step in the algorithm. We present the results of a simulation study highlighting that our simulation algorithm works as expected and is highly accurate and efficient, such that it clearly outperforms customary approximate sampling schemes. As a byproduct, we also develop here new max-id models, which can be represented as pointwise maxima of general location scale mixtures, and which possess flexible tail dependence structures capturing a wide range of asymptotic dependence scenarios.
翻译:在极端值理论中,最大值(最大偏差)进程在极值理论中发挥着核心作用,包括了所有最稳定过程的亚类。它们允许根据从适合的功能空间定义的 Poisson 点进程产生的随机功能的组件最大值进行建设性代表。从最大值进程中模拟往往因其复杂的随机结构而困难重重,而高度计算其联合密度在数字上往往不可行。因此,最大值进程精确而高效的模拟技术是研究进程特点和绘制统计推断的有用工具。在最大值进程的模拟算法的启发下,我们在这里开发了理论和算法,以便根据某些(现有或新的)最大值进程的灵活(现有或新的)类别,对模拟方法进行总体模拟,可以通过采用适应性拒绝抽样方法,绕过算法中的数字整合步骤。我们介绍了模拟研究的结果,强调我们的模拟算法工作是预期的,并且非常准确和高效,因此,它明显超越了最高值的模型的典型依赖性假设,因此,我们这里的模型是典型的典型的、具有最高值的模型,作为最高值的模型的模型,作为一个产品,也是一个总级的模型的模型的模型的模型,其最高值。