题目： Testing high-dimensional covariate effects in the presence of covariate heterogeneity

主讲人：朱利平
讲座时间：2023年6月16日（周五）9:30-10:30
地点：综合楼644会议室
报告人简介：

朱利平，中国人民大学杰出学者特聘教授，统计与大数据研究院院长、教授、博士生导师。
朱利平教授长期从事大数据统计学基础理论研究，研究领域包括高维及超高维数据分析、非线性相依数据分析等。
朱利平教授入选国家高层次人才计划，获得国家杰出青年科学基金支持。受邀担任《统计年刊》、《多元统计分析》等多个国际国内学术期刊编委、副主编或领域主编。现任中国现场统计研究会高维数据统计分会和生存分析分会副理事长。

报告摘要：
In this talk, I introduce several  tests for the mean 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-invariance, 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-invariance 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.