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.
