【专家简介】：郑术蓉，东北师范大学教授，博士生导师。主要从事大维随机矩阵理论及高维统计分析的研究。主要兴趣包括：大维随机矩阵谱性质、高维假设检验、高维因子分析、高维判别分析等。曾在Annals of Statistics, JASA, Biometrika等统计学重要学术期刊上发表多篇跟大维随机矩阵有关的学术论文。
【报告摘要】：This paper proposes a test statistic for two sample mean testing problems for high dimensional data by assuming the linear structure on high dimensional precision matrices. A new precision matrix estimation method considering its linear structure is first proposed, and the regularization method is implemented to select the true basis matrices that can further reduce the approximation error. Then the test statistic is constructed by imposing the estimation of the precision matrix. The proposed test is valid for both the low dimensional setting and high dimensional setting even if the dimension of the data is greater than the sample size. The limiting null distributions of the proposed test statistic under both null distribution and alternative distribution are derived. Extensive simulations are conducted for estimating the precision matrix and testing difference of the high dimensional mean vector. Simulation results show that the proposed estimation method enjoy low estimation error for the precision matrix and the regularization method is able to efficiently select the import basis matrix. The testing method perform well compared with the existing methods especially when the elements of the vector have unequal variances. A real data example is then provided to demonstrate the potential of the proposed method in real world applications.
【报告时间】：2024年12月11日 10:30-11:30
【报告地点】：位育楼417
