Rank-based Procedures for Structural Hypotheses on Covariance Matrices

A wide class of structural models on multivariate normal covariance matrices can be expressed using symmetries. For example, a multivariate normal vector has the intraclass correlation structure (where all variances are equal, and all covariances are equal) if the covariance matrix is invariant under permutation of the components, and the components are independent if the covariance matrix in invariant under sign changes of the components. In general, symmetry models are given by requiring the covariance to be invariant under the action of a subgroup of the orthogonal group. Such models include the independent and identically distributed (iid) model, compound symmetry models (which are extensions of the intraclass correlation model),