On monotonicity of the modified likelihood ratio test for the equality of two covariances

AbstractFor testing the hypothesis of equality of two covariances (Σ1 and Σ2) of two p-dimensional multivariate normal populations, it is shown that the power function of the modified likelihood ratio test increases as λ1 increases from one and λr decreases from one where λ1 > … > λr > 0 are the distinct characteristic roots of Σ1Σ2−1, r ≤ p. As a by-product we get the unbiased result already established by Sugiura and Nagao (1968)