Independence-distribution-preserving dependency structures for the modified likelihood ratio test for detecting unequal covariance matrices

The modified likelihood ratio (MLR) test statistic is frequently used to detect unequal covariance matrices. We are concerned with examining this statistic with respect to departures from the usual i.i.d. assumptions on the sample data. In particular we characterize the joint covariance structure of two groups of multivariate normal observations so that the distribution of this MLR test statistic is identical to that under the usual assumption of independent identically distributed observations.