報告人：張正軍（中國科學院大學）

報告題目：New extreme value theory for maxima of maxima

報告摘要：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.

報告時間：2024年10月17日（星期四）15:30-17:00

報告地點：科技樓南706室

邀請人：潘燈

報告人簡介：張正軍教授現為中國科學院大學經濟與管理學院長聘教授和統計與數據科學系主任，中國科學院預測科學研究中心副主任，原美國威斯康辛大學統計系終身教授和系副主任，國際數理統計協會執行委員和财務總監（July 2016 -- July 2022），國際數理統計協會會士，美國統計協會會士。現擔任JASA，JBES， Statistica Sinica， JDS， EJS、STaRF等國際期刊副主編。主要研究方向包括統計理論和方法、計量經濟學、金融計量學、計算醫學與實踐、 仿真優化、極端氣候等等。在國際頂級期刊：統計（AoS，JASA，JRSSB）、計量（JoE, EE）、金融（JBES, JBF）、優化與控制（Automatica）、醫學（AFM， Vaccines、npj PO）、氣象 (ATM) 等發表論文上百篇。代表性工作和首創性思想和作品包括: 新極值理論、絕對和相對同步有效性（AbRelaTEs）、雙邊截斷極值懲罰變量選擇機器學習模型（TWT-LR-ETP）、商相關系數（QCC、TQCC）、非對稱廣義相關系數（GMC）、滞後尾部相依系數(lambda_k)、最大線性回歸模型(MaxLR)、最大邏輯回歸模型(Max-logistic)、EGB2期權定價公式、盯市在險價值（MMVaR）、條件極值Frechet自回歸（AcF）, 虛拟标準數字貨币（VSTC），新冠基因組學、癌症基因組學的幾何空間（DARPA： Mathematical Challenge Fifteen: The Geometry of Genome Space），等等。