Statistics Seminar（2014-06）

Topic:Simulation-Based Hypothesis Testing of High Dimensional Means Under General Dependency — An alternative road to high dimensional tests

Speaker:Dr.Jinyuan Chang,the University of Melbourne

Time:Thursday, 20 March, 14:00-15:00

Location:Room 217, Guanghua Building 2

Abstract:High dimensional hypothesis testing for mean vectors has emerged in various scientific fields, and also stimulated many innovative methods in statistics. In this paper, we introduce a simulation-based (Monte Carlo-based) procedure for testing high dimensional means with little restrictions on dependence structures. The new testing procedure is based on $L^infty$ statistics and the Gaussian approximation to empirical processes, by which we are free from imposing explicit assumptions on dependency. For both one-sample and two-samples problems, test statistics are constructed, for which the convergence rate, limiting size and power are analyzed. A marginal screening procedure is proposed to assist new test statistics on testing sparse alternatives,where the screening consistency and asymptotic power are examined. Numerical studies are conducted to assess the performance of the testing procedure and compare it with existing tests in literature.

About the speaker:Dr. Jinyuan Chang is a research fellow at the Department of Mathematics and Statistics, the University of Melbourne, Australia. He received his Ph.D. from Peking University and a B.S. from Beijing Normal University. He is also a recipient of ZHONG Jiaqing Mathematics Award (2013) and Laha Travel Award (2012). His research area includes Empirical Likelihood and its Application, Financial Econometrics, High Dimensional Data Analysis and Functional Data Analysis.