Mathematical Sciences: Research in Multivariate StatisticalAnalysis

数学科学：多元统计分析研究

• 批准号: 9203922
• 负责人: Robb Muirhead
• 金额: $ 4万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-08-01 至 1995-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9203922&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Multivariate; StatisticalAnalysis

A central question in multivariate data analysis is the number of factors, usually couched in terms of the "true" rank of the covariance matrix. A variety of optimality criteria can be applied to the sample covariance matrix; and these are in fact the basis for many standard multivariate inferential procedures including principal components analysis, factor analysis, multivariate analysis of variance and discriminant procedures. This research will examine various model selection methods, giving special attention to robustness. New approaches to discriminant analysis will be drawn using ideas from projection pursuit. Researchers analyzing observations on many variables simul- taneously face the problem of deciding how many factors are really important. The statistical procedures used to assess the e number of important factors needs to be stable in the presence of normal variation present in the data. This research focusses on desirable new methods to determine the number of such factors and also on methodology to identify interesting features in the data when many variables are observed at the same time for only a moderate number of individuals.

多元数据分析中的一个中心问题是 许多因素，通常用“真实”等级来表达， 协方差矩阵。 可以使用各种最优性标准， 应用于样本协方差矩阵;这些实际上是 许多标准多元推理程序的基础 包括主成分分析，因子分析， 多变量方差分析和判别程序。 本研究将探讨各种模型选择方法， 特别注意鲁棒性。 的新办法 判别分析将使用投影的思想来绘制 追求 研究人员分析了许多变量的观察结果， 我们面临着决定有多少因素 非常重要 用于评估的统计程序 许多重要因素需要在存在的情况下保持稳定， 数据中存在的正常变化。 这项研究的重点是 确定这些因素数量的理想新方法 以及确定《公约》中令人感兴趣的特点的方法 数据时，许多变量被观察到在同一时间只有一个 中等数量的个体。