A test for the equality of covariance matrices when the dimension is large relative to the sample sizes

A simple statistic is proposed for testing the equality of the covariance matrices of several multivariate normal populations. The asymptotic null distribution of this statistic, as both the sample sizes and the number of variables go to infinity, is shown to be normal. Consequently, this test can be used when the number of variables is not small relative to the sample sizes and, in particular, even when the number of variables exceeds the sample sizes. The finite sample size performance of the normal approximation for this method is evaluated in a simulation study.