• ## 统计与管理学院2018年学术报告第9期

【主 题】 Testing independence with high-dimensional correlated samples

【报告人】 刘卫东 教授

上海交通大学

【时 间】 2018年03月16日（星期五）10:00-11:00

【地 点】 上海财经大学统计与管理学院大楼1208会议室

摘 要】Testing independence among a number of (ultra) high-dimensional random samples is a fundamental and challenging problem. By arranging $n$ identically distributed $p$-dimensional random vectors into a $p \times n$ data matrix, we investigate the testing problem on independence among columns under the matrix-variate normal modeling of the data. We propose a computationally simple and  tuning free test statistic, characterize its limiting null distribution, analyze the statistical power and prove its minimax optimality. As an important by-product of the test statistic, a ratio-consistent estimator for the quadratic functional of covariance matrix from correlated samples is developed. We further study the effect of correlation among samples to an important high-dimensional inference problem --- large-scale multiple testing of Pearson's correlation coefficients. It can be shown that blindly using classical inference results based on the sample independence assumption will lead to many false discoveries, which suggests the need for conducting independence testing before applying existing methods. To address the challenge arising from the correlation among samples in correlation test,  we propose a sandwich estimator" of Pearson's correlation coefficient by de-correlating the samples, based on which the resulting  multiple testing procedure asymptotically controls the overall false discovery rate at the nominal level while maintaining good statistical power. Both simulated and real data experiments are carried out to demonstrate the advantages of the proposed methods.