Mathematical Sciences: Order Restricted Inference in Multivariate Variance Components Models

该研究涉及到使用基于问题的Fenchel对偶表述的方法来研究非平衡多元方差成分模型的估计。工作将集中在多元方差成分模型中协方差矩阵的估计和检验，将结果与适当的统计领域联系起来，并研究所提出算法的收敛速度。多元随机效应模型涉及随机效应的协方差矩阵非负定的约束，这导致了矩阵的低阶。本文将研究这些矩阵的限制极大似然估计的算法。

The research involves the study of estimation in unbalanced multivariate variance components models using an approach based on a Fenchel duality formulation of the problem. The effort will be concentrated in estimation and testing of covariance matrices in multivariate variance component models, relating the results to appropriate fields of statistics, and studying rates of convergence of the proposed algorithms. The multivariate random effects model involves constraints that the covariance matrices of the random effects be nonnegative definite which leads to a Lowner ordering of matrices. Algorithms will be investigated find to the restricted maximum likelihood estimators of such matrices.