Prof Runze Li’s Bio

Runze Li is Verne M. Willaman Professor of Statistics, The Pennsylvania State University. He is a fellow of IMS and ASA. He was the co-editor of the Annals of Statistics from 2013-2015 and is an associate editor of Journal of American Statistical Association since 2006. His current researches concentrate on developing effective statistical procedures for high-dimensional data analysis, including variable selection, feature screening and hypothesis testing. He is also interested in applying these statistical procedures for analyzing real-life high-dimensional data such as genetic data analysis and functional MRI data analysis. His other research interests include non- and semi-parametric modeling and statistical applications to scientific research in social behavioral science and engineering.

Title: Projection Test for High-Dimensional Mean Vectors with Optimal Direction

Abstract: Testing the population mean is fundamental in statistical inference. When the dimensionality of a population is high, traditional Hotelling's T2 test becomes practically infeasible. In this paper, we propose a new testing method for high-dimensional mean vectors. The new method projects the original sample to a lower-dimensional space and carries out a test with the projected sample. We derive the theoretical optimal direction with which the projection test possesses the best power under alternatives. We further propose an estimation procedure for the optimal direction, so that the resulting test is an exact t-test under the normality assumption and an asymptotic chi-square test with 1 degree of freedom without the normality assumption. Monte Carlo simulation studies show that the new test can be much more powerful than the existing methods, while it also well retains Type I error rate. The promising performance of the new test is further illustrated in a real data example.