Prof.  Jin Ting  Zhang
National University of Singapore,  Singapore

Title: Two-sample tests for equal distributions in separate metric space:maximum mean discrepancy based approaches

Abstract:

Testing the equality of two distributions based on two independent samples generated in some separable metric space  is a fundamental hypothesis testing problem in statistics.  It  is  broadly applicable in identifying  similarity or distinction of two complicated  data sets (e.g., high-dimensional data or functional data)  collected in a wide range of research or industry areas, including biology, bioinformatics, medicine, material science,  among others.  Recently  a  so-called maximum mean discrepancy (MMD) based approach for the above two-sample problem  has been proposed, resulting in several interesting tests. However, the main theoretical and numerical results of these MMD based  tests depend on a very restricted  assumption that the two samples have the same sample sizes. In real data analysis, this equal-sample-size assumption is hardly satisfied and discarding  some of the observations often means  a loss of priceless  information. In this talk, we give  a brief review of the  MMD based tests and propose  a new  MMD based test with the equal-sample-size  assumption removed. The asymptotic null and alternative distributions of the MMD based test statistic and its root-n consistency  are established. Methods for approximating the null distribution, resulting in easy and quick implementation, are proposed.    Numerical experiments based on artificial data  and six real data sets from different areas of applications demonstrate that  the resulting test  works very well in terms of size control and power, when  it is  compared with several existing competitors. (This is a joint work with Dr.  Smaga,  Adam Mickiewicz University, Poland.)

Biography:

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 Full  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 70 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.