统计学系系列讲座之286-287期

统计学系系列讲座之286期

时　间：2018年3月19日（周一）14:00-15:00

地　点：史带楼205室

主持人：张新生 教授 复旦大学管理学院统计学系

主　题：Testing independence with high-dimensional correlated samples

主讲人：刘卫东 教授   上海交通大学自然科学研究院

简　介：刘卫东博士2008年在浙江大学获博士学位，2008-2011年在香港科技大学和美国宾夕法尼亚大学沃顿商学院从事博士后研究。研究领域为高维数据的统计推断，在统计学四大顶级期刊 AOS,JASA,JRSSB,Biometrika 和概率论顶级期刊 AOP,PTRF等发表四十余篇论文。曾获得国家优秀青年科学基金，入选国家“万人计划”青年拔尖人才计划。

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.

统计学系系列讲座之287期

时　间：2018年3月22日（周四）09:00-10:00

地　点：史带楼205室

主持人：夏寅 青年研究员 复旦大学管理学院统计学系

主　题：Multiple change-points detection in high dimension

主讲人：王兆军 教授　南开大学统计研究院

简　介：王兆军，南开大学统计研究院教授、博导、副院长，教育部**学者特聘教授。任中国现场统计研究会常务理事；中国统计教育学会高等教育分会副会长等职务。担任《数理统计与管理》副主编；《应用概率统计》编委。其主要研究方向包括统计过程控制、非（半）参数回归、降维、高维数据分析、变点等。 

摘　要：Change-point detection is an integral component of statistical modeling and estimation. For high-dimensional data, classical methods based on the Mahalanobis distance are typically inapplicable. We propose a novel testing statistic by combining a modified Euclidean distance and an extreme statistic, and its null distribution is asymptotically normal. The new method naturally strikes a balance between the detection abilities for both dense and sparse changes, which gives itself an edge to potentially outperform existing methods. Furthermore, the number of change-points is determined by a new Schwarz’s information criterion together with a pre-screening procedure, and the locations of the change-points can be estimated via the dynamic programming algorithm

in conjunction with the intrinsic order structure of the objective function. Under some mild conditions, we show that the new method provides consistent estimation with an almost optimal rate. Simulation studies show that the proposed method has satisfactory performance of identifying multiple change-points in terms of power and estimation accuracy, and two real data examples are used for illustration.

统计学系 

2018-3-14