pMAX随机场
pMAX Random Fields
摘要：
在工程、气候学、金融、精算等若干领域，发生非典型现象的风险是一个贯穿各领域的问题。极值理论是探讨这一主题的自然工具。这些随机现象中的许多都带有在时间和空间中定义的变量，通常通过随机场建模。因此，极值背景下的随机场的研究变得势在必行，特别是在过去的十年中，随机场的研究得到了发展。在这项工作中，我们提出了一个新的随机场，称为pMAX，设计用于建模极端。我们通过相应的二元尾相关系数分析了它的相关性和前渐近相关结构。得到了模型参数的估计，并分析了它们的有限样本性质。仿真实例说明了结果。
英文摘要：
The risk of occurrence of atypical phenomena is a cross-cutting concern in several areas, such as engineering, climatology, finance, actuarial, among others. Extreme value theory is the natural tool to approach this theme. Many of these random phenomena carry variables defined in time and space, usually modeled through random fields. Thus, the study of random fields in the context of extreme values becomes imperative and has been developed especially in the last decade. In this work, we propose a new random field, called pMAX, designed for modeling extremes. We analyze its dependence and pre-asymptotic dependence structure through the corresponding bivariate tail dependence coefficients. Estimators for the model parameters are obtained and their finite sample properties analyzed. Examples with simulations illustrate the results.
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