High Dimension - Low Sample Size Statistical Analysis

摘要提出在医学图像分析和基因表达微阵列分析领域进行研究。这些看似不同的领域有一个共同的结构。包含这两者的总体抽象是“高维-低样本大小”（HDLSS）。HDLSS数据完全超出了经典统计多元分析的范围，因为“数据球体化”的关键第一步不再执行。这激发了一个非常大的新统计方法工具箱的发展，它将在远远超出那些推动这项研究的领域有用。所提出的分析工作的一个重要部分是开发了一种全新类型的渐近分析，其中样本量是固定的，并且维数趋于无穷。拟议的研究将是关于发展和评估新的数据分析方法。这将为应对当前医学领域主要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。第二个挑战是使快速发展的医学成像技术的突破对执业医疗专业人员更有用。这两个领域都将从这项研究过程中发展出来的具有创造性的统计分析新方法中得到很大的好处。

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.