New extreme value theory for maxima of maxima
New extreme value theory for maxima of maxima
复制标题
DOI：
10.1080/24754269.2020.1846115
复制
发表时间：
2020-12
影响因子：
0.5
通讯作者：
Wenzhi Cao;Zhengjun Zhang
中科院分区：
文献类型：
--
作者：
Wenzhi Cao;Zhengjun Zhang
虽然提出了先进的统计模型来更好地拟合复杂的数据，但是科学技术的进步产生了更复杂的数据，例如大数据，现有的概率论和统计模型在这些数据中发现了局限性。这项工作为研究混合过程中产生的数据的极值建立了概率基础，混合模式取决于样本长度和数据生成源。特别地，我们证明了具有上述混合模式的随机变量序列的极大值的极大值的极限分布，称为加速极大稳定分布，是三种类型的极值分布的乘积。因此，我们的理论结果比经典的极值理论更具通用性，可以适用于大数据相关问题的研究。给出了一些例子来直观地说明新的分布族。我们还建立了一组随机变量具有极限分布的混合条件。给出了相关独立序列和任意区间上的极大值的结果。我们用仿真证明了我们新建立的极大极值理论的优点。
Although advanced statistical models have been proposed to fit complex data better, the advances of science and technology have generated more complex data, e.g., Big Data, in which existing probability theory and statistical models find their limitations. This work establishes probability foundations for studying extreme values of data generated from a mixture process with the mixture pattern depending on the sample length and data generating sources. In particular, we show that the limit distribution, termed as the accelerated max-stable distribution, of the maxima of maxima of sequences of random variables with the above mixture pattern is a product of three types of extreme value distributions. As a result, our theoretical results are more general than the classical extreme value theory and can be applicable to research problems related to Big Data. Examples are provided to give intuitions of the new distribution family. We also establish mixing conditions for a sequence of random variables to have the limit distributions. The results for the associated independent sequence and the maxima over arbitrary intervals are also developed. We use simulations to demonstrate the advantages of our newly established maxima of maxima extreme value theory.