Mathematical Sciences: Research in Multivariate Statistical Analysis

数学科学：多元统计分析研究

• 批准号: 8902225
• 负责人: Robb Muirhead
• 金额: $ 11.82万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-01 至 1993-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902225&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Multivariate; Statistical

Research in multivariate statistical analysis will focus on problems related to the eigenstructure of random and parameter matrices. Inference problems in principal components, factor analysis, canonical correlations, multivariate analysis of variance and discriminant analysis that involve sequential testing of nested hypotheses will be examined. Ways of improving the testing procedures will be studied. Another focus of research is the estimation of the eigenstructures with the emphasis on the development of optimal, accurate and reliable estimates of eigenvalues in multivariate analysis of variance, multiple discriminant analysis and canonical correlation analysis. The technique of shrinking standard estimates towards some central value will be examined. Another topic of research is concerned with robustness and focuses on the use of projection pursuit techniques in the area of discriminant analysis.

多元统计分析的研究将集中在与随机矩阵和参数矩阵的特征结构有关的问题。推理问题在主成分，因素分析，典型相关，方差的多变量分析和判别分析，涉及嵌套假设的顺序测试将被检查。将研究改进检测程序的方法。另一个研究重点是特征结构的估计，重点是在多变量方差分析、多重判别分析和典型相关分析中开发最优、准确和可靠的特征值估计。将研究将标准估计缩小到某个中心值的技术。另一个研究主题与鲁棒性有关，并着重于在判别分析领域使用投影追踪技术。