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.
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。