极大值的极大值的新极值理论

IF 0.7 Q3 STATISTICS & PROBABILITY
Wenzhi Cao, Zhengjun Zhang
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引用次数: 11

摘要

尽管已经提出了先进的统计模型来更好地拟合复杂数据,但科学技术的进步已经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其中发现了它们的局限性。这项工作为研究混合过程中产生的数据的极值奠定了概率基础,混合模式取决于样本长度和数据产生源。特别地,我们证明了具有上述混合模式的随机变量序列的最大值的极限分布,称为加速最大稳定分布,是三种极值分布的乘积。因此,我们的理论结果比经典的极值理论更具一般性,可以应用于大数据相关的研究问题。举例说明了新分布族的直观性。我们还建立了一系列随机变量具有极限分布的混合条件。还得到了相关独立序列和任意区间上的最大值的结果。我们使用模拟来证明我们新建立的极大值极值理论的优势。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
New extreme value theory for maxima of maxima
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.
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来源期刊
CiteScore
0.90
自引率
20.00%
发文量
21
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