Classical multivariate analyses are typically designed for fixed dimensional data, and are often not applicable, even invalid, for high-dimensional data. Analysis of modern high-dimensional data call for novel multivariate statistical approaches in the "large-p, small n" paradigm. This proposal consists of three broad objectives aiming to establish a set of multivariate inferential procedures that are adaptive to high dimensionality, and can accommodate a wide range of model and dependence structures. The investigators will develop new thresholding methods to improve the power performance of the tests for high dimensional means and covariance when the signals are sparse and faint. They also propose bandwidth estimators for the state of the art banding and tapering estimators for covariances, and hence make these two estimation approaches practical. The project will also develop tests for nonparametric functions of high-dimensional covariates in partially linear models.
The multivariate testing procedures obtained from the proposed projects will be readily applicable in selecting gene-sets which are associated with phenotype variations, or responsive to certain treatments in the forms of having different means or covariance. The successful application in gene-set analysis will enhance our understanding of gene regulations at a biological meaningful pathway level. The research will also improve the applications of multivariate analysis in biology, marketing research, and financial risk management.
