勷勤数学•专家报告

题      目：Spectral Properties of High-dimensional Rescaled Sample Correlation Matrices under Elliptical Distributions

报  告  人： 邹婷婷 讲师  (邀请人：吴琴)

                                    吉林大学

时      间： 5月17日  09：00-10:00

地     点：数科院西楼二楼会议室

报告人简介:

        邹婷婷，吉林大学数学学院讲师。主要研究方向为大维随机矩阵理论与高维统计推断，现主持国家自然科学基金青年项目C类，成果发表于Bernoulli, Statistica Sinica, CSDA, EJS等期刊，现为JMVA的Early Career Advisory Board成员。

摘      要：

       Under the convergence regime that the data dimension and sample size tend to infinity proportionally, we establish the joint central limit theorem for the linear spectral statistics of the rescaled sample correlation matrices when the population follows an elliptical distribution. This general theoretical result has wide applications. As an illustration, we consider testing whether a high-dimensional correlation matrix equals to a prespecified matrix. We first propose three test statistics based on the quadratic norm and then derive their limiting distributions. To enable the practical applications of the proposed tests, we also develop a numerical approach for computing the asymptotic variances and covariances in the central limit theorem. Furthermore, extensive simulation studies are systematically conducted to evaluate the finite sample performance of the proposed testing procedures.

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