报告题目：Sampling without replacement from a high dimensional finite population

报 告 人：张阳春 教授

报告人单位：上海大学

报告时间：2025年9月11日 星期四 上午10:00-11:00

报告地点：腾讯会议：844 702 286

校内联系人：丁雪 [email protected]

报告摘要： It is well known that most of the existing theoretical results in statistics are based on the assumption that the sample is generated with replacement from an infinite population. However,in practice, available samples are almost always collected without replacement. If the population is a finite set of real numbers, whether we can still safely use the results from samples drawn without replacement becomes an important problem. In this paper, we focus on the eigenvalues of high-dimensional sample covariance matrices generated without replacement from finite populations. Specifically, we derive the Tracy-Widom laws for their largest eigenvalues and apply these results to parallel analysis. We provide new insight into the permutation methods proposed by Buja and Eyuboglu in [Multivar Behav Res. 27(4) (1992) 509–540]. Simulation and real data studies are conducted to demonstrate our results.

报告人简介：上海大学理娱乐城副教授，硕士生导师。研究领域为高维统计、随机矩阵、 强化学习。博士毕业于哈尔滨工业大学，并在新加波国立大学联合培养。先后在新加坡国立大学、新加坡南洋理工大学、香港科技大学等学校访问。主持和参与多项基金项目，包括上海市“科技创新行动计划”扬帆计划，国家自然科学基金青年基金和面上项目。目前已发表SCI论文20余篇，指导学生发表中科院一区SCI论文三篇，CCF A类会议一篇，CCF B 类会议一篇，中国数学会T2级别文章一篇 。