Mathematical Sciences: Multivariate Variance Components Models and Order RestrictedInference

数学科学：多元方差分量模型和阶数限制推理

• 批准号: 9104673
• 负责人: Richard Dykstra
• 金额: $ 7.49万
• 依托单位: University of Iowa
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-09-01 至 1994-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9104673&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Multivariate; Variance; Components

This project involves estimation in unbalanced multivariate variance components models using an approach based on a Fenchel duality formulation of the problem. The Fenchel approach has been successful in related research projects and is promising for the current project. The research will concentrate in three areas: 1) estimation and testing of covariance matrices in multivariate variance component models; 2) integrating results into related fields of statistics; and 3) studying the rates of convergence of the proposed algorithms. This project is in the general area of statistics and involves the estimation of variance components in both univariate and multivariate linear models. This is an important field of statistical research. Many of the multivariate models are now unavailable to researchers due to the inability of the existing statistical techniques to estimate the variance of components. The research in this project may have significant impact on the ability to utilize these multivariate models.

该项目涉及使用基于问题的Fenchel对偶公式的方法对不平衡多元方差成分模型进行估计。Fenchel方法已经在相关的研究项目中取得了成功，并且在当前的项目中很有前景。研究将集中在三个方面：1)多元方差成分模型中协方差矩阵的估计与检验；2)将结果整合到相关的统计领域；3)研究算法的收敛速度。这个项目属于统计学的一般领域，涉及单变量和多变量线性模型中方差成分的估计。这是统计研究的一个重要领域。由于现有的统计技术无法估计成分的方差，许多多变量模型现在对研究人员来说是不可用的。本项目的研究可能会对这些多变量模型的运用能力产生重大影响。