Prof. Jin-Ting Zhang
National University of Singapore, Singapore
Title: Normal-Reference Tests for High-Dimensional Hypothesis Testing
Abstract:
In the past two decades, much attention has been paid for high-dimensional hypothesis testing. Several centralized or non-centralized L2-norm based test statistics have been proposed. Most of them imposed strong assumptions on the underlying covariance structure of the high-dimensional data so that the associated test statistics are asymptotically normally distributed. In real data analysis, however, these assumptions are hardly checked so that the resulting tests have a size control problem when the required assumptions are not satisfied. To overcome this difficulty, in this talk, we investigate a so-called normal-reference test which can control the size well. In the normal-reference test, the null distribution of a test statistic is approximated with that of a chi-square-type mixture which is obtained from the test statistic when the null hypothesis holds and when the samples are normally distributed. The distribution of the chi-square-type mixture can be well approximated by a three-cumulant matched χ2-approximation with the approximation parameters consistently estimated from the data. Two simulation studies demonstrate that in terms of size control, the proposed normal- reference test performs well regardless of whether the data are nearly uncorrelated, moderately correlated, or highly correlated and it performs much better than two existing competitors. A real data example illustrates the proposed normal-reference test.
KEY WORDS: χ2-type mixtures; high-dimensional data; three-cumulant matched χ2-approximation; two-sample Behrens–Fisher problem.
Biography:
Professor
Zhang Jin-Ting is from Guangdong Province, China. He obtained his bachelor's
degree from Peking University in 1988, his master's degree from the Institute
of Applied Mathematics of the Chinese Academy of Sciences in 1991, and his
Ph.D. from the University of North Carolina at Chapel Hill in 1999. Professor
Zhang conducted postdoctoral research at Harvard University and served as a
senior visiting scholar at several universities, including Princeton and
Rochester in the United States. He is currently a tenured professor in the
Department of Statistics and Data
Science at the National University of Singapore, where he also mentors Ph.D.
students and postdoctoral researchers.
To
date, Professor Zhang has supervised ten master's students, ten Ph.D. students,
and nine postdoctoral research fellows. He has published over 80 academic
papers, authored two monographs on statistics, and edited one volume of
collected academic papers. He currently serves, or has served, as an associate
editor or editorial board member for several academic journals. Additionally,
he has been part of the organizing committee for six major international
conferences. His current research areas include nonparametric statistics,
longitudinal data analysis, functional data analysis, high-dimensional data
analysis, and more.