Mathematical Sciences: Order Restricted Inference in Multivariate Variance Components Models

本研究涉及非均衡估计的研究， 多变量方差分量模型，使用基于 关于这个问题的Fenchel对偶公式 的努力 将集中于估计和检验协方差 多变量方差分量模型中的矩阵， 结果，以适当的统计领域，和学习率 所提出的算法的收敛性。多元 随机效应模型包含协方差 随机效应的矩阵是非负定的， 导致了矩阵的Lowner排序。算法将 对约束极大似然估计的研究发现 这样的矩阵。

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.