Department Seminar by Xiufan Yu

Please Note: This seminar will be given online.

Power Enhancement in High-Dimensional Hypothesis Testing

In recent years, power-enhanced tests with high-dimensional data have received growing attention in theoretical and applied statistics. Various tests possess different high-power regions. In practice, we may lack prior knowledge about the alternatives when testing for a problem of interest. For example, when identifying sets of differentially expressed genes, the disparities among gene-sets are potentially reflected by the average or the variation of gene expression levels. It is important to derive powerful testing procedures against more general alternatives.

In this talk, I will focus on power enhancement in jointly testing two-sample mean vectors and covariance matrices of high-dimensional data. Existing works mainly focus on testing mean vectors or covariance structures instead of testing both aspects together. To address this challenge, I will present a new power-enhanced simultaneous test. The proposed test is powerful in detecting either mean differences or covariance differences under either sparse or dense alternatives. Theoretical analyses prove the accurate asymptotic size and consistent asymptotic power of the proposed test against more general alternatives, and simulation studies demonstrate the finite-sample performance. Moreover, I apply the proposed test in a real application to find differentially expressed gene-sets in cancer studies, which confirms the prodigious performance of the proposed test with the support of biological evidence.