Asymptotic results for decomposing a likelihood-ratio statistic into separate components

AbstractThis paper shows how the likelihood ratio for testing the equality of two variance-covariance matrices decomposes asymptotically into two separate tests, one for equality of the latent roots or eigenvalues, and the other for equality of the eigenvectors. The decomposition develops from the role of the orthogonal group and its related Lie algebra in multivariate normal theory