Mathematical Sciences: Multivariate Variance Components Models and Order RestrictedInference

这个项目涉及非平衡多元估计 方差分量模型使用的方法的基础上Fenchel 问题的对偶形式。 Fenchel的方法一直是 在相关研究项目中取得成功，并有望为 当前项目。 本研究将集中在三个方面：1） 多元协方差矩阵的估计和检验 方差分量模型; 2）将结果整合到相关的 统计学领域; 3）研究收敛速度 提出的算法。 该项目属于一般统计领域， 方差分量的估计在单变量和 多元线性模型 这是一个重要的领域， 统计研究。 许多多变量模型现在 由于现有的研究人员无法 统计技术来估计组件的方差。 的 本项目的研究可能会对能力产生重大影响 来利用这些多变量模型。

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.