Analysis of high-dimensional data has emerged as one of the most important and active areas of research in statistics. In particular, hypothesis testing for high-dimensional covariance structures is an interesting and challenging problem with a wide range of applications in areas such as genomics, medical imaging, and the social sciences. The methodology developed in this project will be used to study important problems in genomics and neuroimaging, including identification of interactions between gene pathways and detection of spatial voxels that are activated due to certain experimental stimuli. The proposed methods will be applied to a breast cancer gene expression study and data from fMRI experiments.
In this project, the investigator aims to develop methodology and theory for large-scale multiple testing on high-dimensional covariance structures. The lack of suitable test statistics, as well as the complex entry-wise dependence structures, impose significant methodological and technical challenges not seen in the conventional multiple testing problem. The proposed research is anticipated to make significant contributions to large-scale and high-dimensional inference for covariance structures and its applications to genomics and neuroimaging. Web pages will be created to enable quick access to software implementation of the new methods, as well as technical reports and relevant references.
