High Dimension - Low Sample Size Statistical Analysis

高维度-低样本量统计分析

• 批准号: 0308331
• 负责人: James Marron
• 金额: $ 18.56万
• 依托单位: University of North Carolina at Chapel Hill
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-08-01 至 2007-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0308331&HistoricalAwards=false
• 关键词: Dimension; Low; Sample; Size; Statistical

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.

DMS-0308331 James S.Marron高维-低样本量统计分析摘要提出了在医学图像分析和基因表达微阵列分析领域的研究。这些看似不同的领域有一个共同的结构。包含两者的总体抽象是“高维-低样本大小”(HDLSS)。HDLSS数据完全不在经典统计多变量分析的范围之内，因为无法再执行关键的第一步--“获取数据”。这推动了一个非常大的新的统计方法工具箱的发展，它将在远远超过那些激励这项研究的领域发挥作用。拟议分析工作的一个重要部分是发展一种全新的渐近分析类型，其中样本量是固定的，并且维度趋于无穷大。拟议的研究将致力于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人员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突破对执业医学专业人员更有用。这两个领域都将从本研究过程中开发的富有创造性的新的统计分析方法中受益匪浅。