Closed Likelihood-Ratio Testing Procedures to Assess Similarity of Covariance Matrices

Different degrees of similarity can be devised among the k covariance matrices Σh, referred to k groups, under the assumption of multivariate normality, using their spectral decomposition. In this paper we introduce a closed testing procedure allowing for a choice between eight patterns of covariances. The new methodology allows to disclose a richer information on the data underlying structure than the classical existing methods, and also a more parsimonious parameterization. An application on a real data set exemplify the proposal and shows its performances