主题：Test the effects of high-dimensional covariates via aggregating cumulative covariances
主讲人：朱利平（中国人民大学）
主持人：姜云卢（暨南大学）
会议时间：2022年9月27日（周二）下午3:00-4:30
会议工具：腾讯会议（ID：895-933-240，密码：202209）
摘要
In this talk, I shall introduce how to test for the effects of high-dimensional covariates on the response. In many applications, different components of covariates usually exhibit various levels of variation, which is ubiquitous in high-dimensional data. To simultaneously accommodate such heteroscedasticity and high dimensionality, we propose a novel test based on an aggregation of the marginal cumulative covariances, requiring no prior information on the specific form 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 under the null hypothesis. We further study the asymptotic relative efficiency of our proposed test with respect to the state-of-art universal tests in two different settings: one is designed for high-dimensional linear model and the other is introduced in a completely model-free setting. A remarkable finding reveals that, thanks to the scale-invariant property, even under the high-dimensional linear models, our proposed test is asymptotically much more powerful than existing competitors for the covariates with heterogeneous variances while maintaining high efficiency for the homoscedastic ones.
主讲人简介
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。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《Statistica Sinica》和《Journal of Multivariate Analysis》等国际学术期刊Associate Editor，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。
