Asymptotic power comparison of three tests in GMANOVA when the number of observed points is large

This paper is concerned with the testing problem of generalized multivariate linear hypothesis for the mean in the growth curve model(GMANOVA). Our interest is the case in which the number of the observed points pp is relatively large compared to the sample size NN. Asymptotic expansions of the non-null distributions of the likelihood ratio criterion, Lawley–Hotelling’s trace criterion and Bartlett–Nanda–Pillai’s trace criterion are derived under the asymptotic framework that NN and pp go to infinity together, while p/N→c∈(0,1)p/N→c∈(0,1). It also can be confirmed that Rothenberg’s condition on the magnitude of the asymptotic powers of the three tests is valid when pp is relatively large, theoretically and numerically.