Song Xi Chen, Iowa State University and Peking University

"Two-sample and ANOVA tests for high dimensional means"

In this paper, we consider testing the equality of two high-dimensional means, motivated by the works of Professor Hall and his collaborators (Hall and Jin, 2010; Delaigle, Hall and Jin 2011). Two techniques are utilized to construct the test statistic for better power performance when the two population mean vectors differ only in sparsely populated coordinates. One is the thresholding to remove the non-signal bearing dimensions. The other is the data transformation via an estimated precision matrix to enhance signal strength. The benefits of the thresholding and the data transformations are showed by an improved power and a wider detection region of the tests. The second objective of this paper is to provide a thresholding-based ANOVA test with data transformation for the equality of multiple-sample means. Simulation experiments and an empirical study are performed to confirm the theoretical findings and to demonstrate the practical implementations. This is a joint work with Jun Li (Kent State University) and Pingshou Zhong (Michigan State University).