报告题目：重尾数据中渐近依赖结构的判别(Distinguish Forms of Asymptotic Dependence in Heavy Tailed Data)

报告人：王天栋，复旦大学上海数学中心青年研究员

报告时间：2025年3月31日16:00- 18:00

报告地点：数学楼2-3会议室

摘要：

In multivariate heavy tail estimation, the support of the limit measure provides information on the asymptotic dependence structure of the random vector with the heavy tail distribution. This asymptotic dependence structure may be difficult to discern, even in favorable cases of bivariate data since exploratory methods can be ambiguous and heavily dependent on threshold choice. We restrict ourselves to techniques that help distinguish between the following asymptotic models for heavy tails in two-dimension: (i) full dependence where the limit measure concentrates on a ray from the origin; (ii) strong dependence where the support of the limit measure is a proper connected subcone of the positive quadrant; (iii) weak dependence where the limit measure concentrates on the whole positive quadrant; (iv) asymptotic independence where the limit measure concentrates on the axes. We propose two test statistics, analyze their asymptotically normal behavior under full and not-full dependence, and discuss method implementation using bootstrap methods. The methodology is illustrated with both simulated and real data.

简介：

王天栋，复旦大学上海数学中心青年研究员，博士生导师。2019年毕业于美国康奈尔大学运筹学与信息工程学院，取得博士学位；2019年9月至2022年8月任职于美国得州农工大学统计系，担任助理教授。2022年9月至今任职于复旦大学上海数学中心，担任青年研究员。2017年以来在Journal of Machine Learning Research, Stochastic Processes and Their Applications, Statistica Sinica等国际学术期刊上发表高水平论文25篇。

邀请人：肖燕妮 教授