报告人：张正军（中国科学院大学）

报告题目：New extreme value theory for maxima of maxima

报告摘要：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. Joint work with Wenzhi Cao.

报告时间：2024年10月17日（星期四）15:30-17:00

报告地点：科技楼南706室

邀请人：潘灯

报告人简介：张正军教授现为中国科学院大学经济与管理学院长聘教授和统计与数据科学系主任，中国科学院预测科学研究中心副主任，原美国威斯康辛大学统计系终身教授和系副主任，国际数理统计协会执行委员和财务总监（July 2016 -- July 2022），国际数理统计协会会士，美国统计协会会士。现担任JASA，JBES， Statistica Sinica， JDS， EJS、STaRF等国际期刊副主编。主要研究方向包括统计理论和方法、计量经济学、金融计量学、计算医学与实践、 仿真优化、极端气候等等。在国际顶级期刊：统计（AoS，JASA，JRSSB）、计量（JoE, EE）、金融（JBES, JBF）、优化与控制（Automatica）、医学（AFM， Vaccines、npj PO）、气象 (ATM) 等发表论文上百篇。代表性工作和首创性思想和作品包括: 新极值理论、绝对和相对同步有效性（AbRelaTEs）、双边截断极值惩罚变量选择机器学习模型（TWT-LR-ETP）、商相关系数（QCC、TQCC）、非对称广义相关系数（GMC）、滞后尾部相依系数(lambda_k)、最大线性回归模型(MaxLR)、最大逻辑回归模型(Max-logistic)、EGB2期权定价公式、盯市在险价值（MMVaR）、条件极值Frechet自回归（AcF）, 虚拟标准数字货币（VSTC），新冠基因组学、癌症基因组学的几何空间（DARPA： Mathematical Challenge Fifteen: The Geometry of Genome Space），等等。