报告题目：Sampling without Replacement from a High Dimensional Finite Population

报告时间：2023-2-21  15:00 - 16:00

报告人：胡江 教授 东北师范大学

报告地点：理学院东北楼四楼报告厅

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.