Collaborative Research: High Dimensional Multivariate Analysis

经典的多变量分析通常是为固定维度的数据设计的，而对于高维数据通常不适用，甚至是无效的。现代高维数据的分析要求在“大p，小n”的范例中采用新的多变量统计方法。这一建议包括三个广泛的目标，旨在建立一套多变量推理过程，这些过程适应高维，并可以适应广泛的模型和依赖结构。研究人员将开发新的阈值方法，以提高信号稀疏和微弱时高维均值和协方差检验的功率性能。他们还提出了最新的带宽估计器、协方差的带状估计器和锥化估计器，从而使这两种估计方法切实可行。该项目还将开发部分线性模型中高维协变量的非参数函数的测试。从拟议项目中获得的多变量测试程序将很容易应用于选择与表型变异有关的基因组，或以具有不同均值或协方差的形式对某些处理作出反应。在基因集分析中的成功应用将在生物学意义的途径水平上加深我们对基因调控的理解。这项研究还将提高多变量分析在生物学、市场研究和金融风险管理中的应用。

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.