REML Estimation of Covariance Matrices with Restricted Parameter Spaces
本文扩展了先前关于方差成分模型的研究，提出一种处理广泛受限参数空间（如协方差矩阵满足特定结构或边界约束）的REML估计方法，适用于平衡与非平衡数据，并通过实例验证。
Abstract Restricted parameter spaces for covariance matrices, such as ∑ = σ2 I or ∑ = αI + βJ, are often used to simplify estimation. In addition, fixed upper and/or lower bounds may be needed to ensure that estimates satisfy a priori hypotheses. With multivariate variance components models, several covariance matrices need to be simultaneously estimated and, even with a reduced parameter space, estimation can be difficult. In earlier work we have discussed estimation for a widely-used class of models where the variance components matrices need only be nonnegative definite. In this article we extend these results to handle a wide class of restricted parameter spaces. We state the conditions required for a parameterization to be a member of the class, discuss the implementation of the results for several different members of the class, and discuss estimation with both balanced and unbalanced data. We give several examples to demonstrate the results.