Estimation and Testing of the Covariance Structure of Doubly Multivariate Data

Abstract

The covariance matrix of doubly multivariate data often has a separable structure, that is, it can be presented as the Kronecker product of two positive definite matrices. In particular, one of the separability components can be further specified, for example, as compound symmetry or autoregression of order one. Another suitable structure for doubly multivariate data is a block compound symmetry structure. In this paper, two testing procedures for such covariance structures, namely the likelihood ratio and Rao score tests, will be discussed. Using simulation studies, it will be shown that the Rao score test outperforms the likelihood ratio test in a number of contexts, mainly for small and moderate sample size. Both of the testing methods will then be illustrated by two real data examples.