On the LBI criterion for the multivariate one-way random effects model under non-normality

The asymptotic null distribution of the locally best invariant (LBI) test criterion for testing the random effect in the one-way multivariable analysis of variance model is derived under normality and non-normality. The error of the approximation is characterized as O(1/n). The non-null asymptotic distribution is also discussed. In addition to providing a way of obtaining percentage points and p-values, the results of this paper are useful in assessing the robustness of the LBI criterion. Numerical results are presented to illustrate the accuracy of the approximation.