Efficiency and robustness in the use of repeated measurements

Efficiencies in repeated-measurements experiments are studied by the use of F statistics when appropriate and of Hotelling's T2 statistics otherwise. Bounds on the asymptotic relative efficiencies of these statistics are given and conditions are found under which one test dominates another uniformly. Similar comparisons are made between T2 and the Lawley-Hotelling T2(0) test in the analysis of repeated vector measurements. It is found that the T2 test may be considerably more efficient than its competitors, but that its efficiency cannot be substantially less. These findings are illustrated numerically by examples from the literature. It is shown further that F and T2 tests are exact for all unimodal distributions constant on ellipsoids, and that efficiency comparisons among F tests are preserved under scale mixtures of multidimensional Gaussian laws.