Upper Limits for Criteria for Tests of Dimensionality Under Elliptical Populations
Abstract In this paper, tests of dimensionality in the multivariate analysis of variance model under elliptical populations are considered. We show that the upper bounds proposed by Yoshida et al. [Yoshida, K., Imai, H., Sato, Y. (2002). New criteria for tests of dimensionality under elliptical populations. J. Japan Statist. Soc. 32:183–192] are upper limits for likelihood ratio (LR), Lawley–Hotelling (LH), and Bartlett–Nanda–Pillai (BNP) criteria under elliptical populations.