Joint Collaborative Statistical Colloquium: Liping Zhu, Renmin University of China

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

Presented by Liping Zhu, Institute Statistics of Big Data, Renmin University of China

Thursday, May 25, 2023
8:00 PM ET
AUST 326
WebEx Link
VooV Link (Meeting ID: 138-225-453)

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.

Speaker Bio:

Dr. Liping Zhu is University Distinguished Professor and Dean of the Institute of Statistics and Big Data at the Renmin University of China. Dr. Zhu obtained his PhD in Statistics from the East China Normal University in 2006. He was a recipient of the National Science Fund for Distinguished Young Scholars. Dr. Zhu has published over 100 papers, including more than 20 in AoS, Biometrika, JASA, and JRSSB. He has supervised 8 PhD students. He served as Associate Editor for AoS and Statistica Sinica. Currently, he is Associate Editor for JMVA, SII, and several other statistical journals.