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数学与统计学院系列学术讲座第十五场
2022-05-18 21:49  

报告题目Test  effects of  high-dimensional covariates via aggregating cumulative covariances

报 告 人: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副院长、博士生导师)

报告时间:2022年5月19日  14:00-15:30

报告地点:腾讯会议  ID:893-5547-7045

校内联系人:付连艳


报告摘要:In this talk, we  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-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.



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副院长、博士生导师,国家高层次人才计划入选者。朱利平一直从事复杂高维数据、超高维数据、非线性相依数据分析方法和理论研究,多篇论文入选高被引论文。

现任中国现场统计学会高维数据分会副理事长、生存分析分会副理事长等,先后受邀担任国际统计学领域顶级学术期刊《The Annals of Statistics》、《Statistica Sinica》、《Journal of Multivariate Analysis》等期刊编委。



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