报告人：李卫明
报告地点：数学与统计学院415室
报告时间：2019年07月03日星期三14:00-15:00
邀请人：胡江
报告摘要：
Distance covariance is a powerful tool for detection of dependence between random vectors. Particularly, uncorrelated but dependent vectors have a positive distance co-variance while their traditional cross-covariance or canonical correlations are all equal to zero. The existing literature on distance covariance is however sparse and limited to low-dimensional scenarios. This paper makes a first step toward a high-dimensional theory for the distance covariance. First we introduce a new random matrix called distance covariance matrix (DCM) whose normalized trace is equivalent to the distance covariance. We first derive a deterministic limit for the eigenvalue distribution of the DCM when the dimensions of the vectors and the sample size tend to infinity simultaneously. This limit is valid when the vectors are independent or weakly dependent through a finite-rank perturbation. It is also universal and independent of the details of the distributions of the vectors. Furthermore, the top eigenvalues of the DCM are shown to obey an exact phase transition when the dependence of the vectors is weak. This finding enables the construction of a new detector for such weak dependence where classical methods based on large sample covariance matrices or sample canonical correlations all fail in the considered high-dimensional framework.
主讲人简介：
李卫明，Associate Professor，现任职于上海财经大学统计与管理学院。研究方向为随机矩阵理论与高维数据分析，在Annals of Statistics，journal of the royal statistical society，series B等著名期刊上发表论文十余篇。
