Abstract

In this talk, we consider hypothesis testing for high dimensional data where the data dimension may be much larger than the sample size so that traditional multivariate tests are no longer applicable. Via imposing strong assumptions on the underlying covariance matrices, most of the existing tests are shown to be asymptotically normal and are conducted using normal approximation. However, in real data analysis, these imposed assumptions may not be satisfied or hardly checked so that these existing tests are less useful. Unlike the existing tests, we proposed simple and adaptive tests. Without imposing strong assumptions on the underlying covariance matrices, the distributions of the proposed tests are shown to be asymptotically chi-squared mixtures and are conducted using chi-square approximation. Good performance of the proposed tests is demonstrated via some simulation studies and a real data example.

About the Speaker

Professor Jin-Ting Zhang was born in Guangdong, China. He got a Bachelor degree in Peking University, China, a Master degree in Academia Sinica, Beijing, China, and a PhD degree in North Carolina University at Chapel Hill, USA. He was a postdoc research fellow at Harvard University. He was a visiting research fellow at University of Rochester and Princeton University, USA. He is a tenured Associate Professor at Department of Statistics and Applied Probability, National University of Singapore. He has trained seven PhD students and a number of postdoc fellows. He has published more than 50 research papers, two monographs, and an edited book of research papers. He has been Associate Editor of a few statistical journals. He served as a member of several scientific committees for several big international conferences. Research areas of Professor Zhang include Nonparametric Regression, Longitudinal data analysis, Functional data analysis and High-dimensional data analysis among others.

Poster