Sampling without replacement from a high dimensional finite population

发布时间：2023-02-22 作者：浏览次数：

Speaker:	胡江	DateTime:	2月22日（周三）16:30-17:30
Brief Introduction to Speaker: 胡江，东北师范大学，教授，博士生导师，入选国家级青年人才。主要从事大维随机矩阵理论与大维统计分析研究。2012年博士毕业于东北师范大学，主持多项国家自然科学基金，发表SCI论文三十余篇，其中包括学科权威期刊Ann. Statist.等，担任SCI杂志 Ran Matrices Theory Appl. 编委。		Place:	6号楼2楼报告厅
Abstract:It is well known that most of the existing theoretical results in statistics is based on the assumption that the sample is generated with replacement from an infinite population. But in practice, the sample in our hand is almost always collected without replacement. If the population is a finite set of real numbers, whether we can still use these results safely for the 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. Simulation and real data studies are conducted to demonstrate the superiority of our results.