讲座主题：Test the effects of  high-dimensionalcovariates via aggregating cumulative covariances

报告人：朱利平（中国人民大学统计与大数据研究院院长，国家杰青，“万人计划”领军人才）

时间：2022年9月22日上午09：00-11：00

线上会议：腾讯会议号920-582-024

报告人简介：朱利平，中国人民大学“杰出学者”特聘教授、博士生导师，统计与大数据研究院院长，国家重大人才工程入选者，国家杰出青年基金获得者,国家“万人计划”领军人才。

朱利平教授长期从事复杂数据分析方法和理论研究工作，在复杂高维、超高维数据领域以及非线性相依数据领域做出了一系列有影响力的研究工作。多篇论文入选ESI高被引论文。现任中国现场统计学会高维数据分会和生存分析分会副理事长，以及多个学会的常务理事、理事等。先后担任统计学领域国际顶级学术期刊《The Annals of Statistics》、国际重要学术期刊《StatisticaSinica》和《Journal of Multivariate Analysis》等国际学术期刊AssociateEditor，以及《系统科学与数学》和《应用概率统计》等国内重要学术期刊编委。

内容摘要：In this talk I shall introduce how to test for the  effects of high-dimensional covariates on theresponse.  In many applications,different components of covariates usually exhibit various levels of variation,which is ubiquitous in high-dimensional data. To simultaneously accommodatesuch heteroscedasticity and high dimensionality, we propose a novel test basedon an aggregation of the marginal cumulative covariances,  requiring no prior information on the specificform of regression models. Our proposed test statistic is scale-invariant,tuning-free and convenient to implement. The asymptotic normality of the proposed statistic is established underthe  null hypothesis. We further studythe asymptotic relative efficiency of our proposed test with respect to thestate-of-art universal tests in two different settings: one is designed forhigh-dimensional linear model and the other is introduced in a completelymodel-free setting. A remarkable finding reveals that, thanks to the scale-invariantproperty, even under the high-dimensional linear models, our proposed test isasymptotically much more powerful than existing competitors for the covariateswith heterogeneous variances while maintaining high efficiency for thehomoscedastic ones.