High Dimension - Low Sample Size Statistical Analysis

DMS-0308331James S. Marron高维低样本统计分析在医学图像分析和基因表达微阵列分析领域提出了研究方向。 这些看似不同的领域有一个共同的结构。 包含这两者的过度抽象是“高维度-低样本大小”（HDLSS）。 HDLSS数据完全超出了经典统计多变量分析的范围，因为关键的第一步“球化数据”不再能够执行。 这促使开发一个非常大的新的统计方法工具箱，这将是有用的领域远远超出那些激励这项研究。 拟议的分析工作的一个重要组成部分是开发一种全新类型的渐近分析，其中样本大小是固定的，维度趋于无穷大。拟议的研究将是开发和评估新的数据分析方法。 这些将为正在应对医学领域当前重大挑战的大型团队提供关键的统计基础设施。 第一个挑战是正在进行的抗癌战争。 第二个挑战是使医学成像技术的迅速发展的突破对执业医学专业人员更有用。 这两个领域都将大大受益于本研究期间将开发的创造性统计分析新方法。

DMS-0308331James S. MarronHigh dimension - low sample size statistical analysisAbstractResearch is proposed in the areas of medical image analysis and the gene expression micro-array analysis. These seemingly divergent fields have a common structure. The over-arching abstraction that contains them both is "High Dimension - Low Sample Size" (HDLSS). HDLSS data are completely outside of the domain of classical statistical multivariate analysis, because the critical first step of "sphering the data" can no longer be performed. This motivates the development of a very large new toolbox of statistical methods, which will be useful in fields far beyond those motivating this research. An important part of the proposed analytical work is the development of a completely new type of asymptotic analysis, where the sample size is fixed, and the dimension tends to infinity.The proposed research will be on the development and assessment of new data analytical methods. These will provide critical statistical infrastructure for the large teams of people that are tackling current major challenges in the field of medicine. The first challenge is the ongoing war on cancer. The second challenge is to make the rapidly developing breakthroughs in medical imaging technology much more useful to practicing medical professionals. Both areas will be substantially benefited by the creative new methods of statistical analysis that will be developed during the course of this research.