Mathematical Sciences: Multivariate Variance Components Models and Order RestrictedInference

这个项目涉及在非平衡多变量方差分量模型中使用一种基于问题的芬切尔对偶公式的方法进行估计。芬切尔方法在相关研究项目中取得了成功，在目前的项目中前景看好。研究将集中在三个方面：1)多元方差分量模型中协方差矩阵的估计和检验；2)将结果整合到相关的统计领域；3)研究所提出的算法的收敛速度。该项目属于一般统计学领域，涉及单变量和多变量线性模型中的方差分量的估计。这是统计研究的一个重要领域。由于现有的统计技术不能估计成分的方差，许多多元模型现在对研究人员来说是不可用的。该项目的研究可能会对利用这些多变量模型的能力产生重大影响。

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.