Liping Zhu (朱利平) received his bachelor's degree from East China Normal University in 2001 and his Doctor's degree from East China Normal University in 2006. He is now distinguished professor and doctoral supervisor of Renmin University of China. And he is the dean of Statistics and Big Data Research Institute and selected by the National Major Talent Project.  He successively served as the associate editor of important international academic journals in the field of Statistics, such as The Annals of Statistics, Statistica Sinica and Journal of Multivariate Analysis, and editorial board members of important domestic academic journals such as "Journal of Systems Science and Mathematical Sciences" and "Chinese Journal of Applied Probability and Statistics".

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

Abstract: 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.