Large sample approximations for the LR statistic for equality of the smallest eigenvalues of a covariance matrix under elliptical population

This paper is concerned with large sample approximations of the LR statistic for testing the hypothesis that the smallest eigenvalues of a covariance matrix are equal. Under a normal population Lawley [1956. Tests of significance for the latent roots of covariance and correlation matrices. Biometrika 43, 128–136.] and Fujikoshi [1977. An asymptotic expansion for the distributions of the latent roots of the Wishart matrix with multiple population roots. Ann. Inst. Statist. Math. 29, 379–387.] obtained a Bartlett-correction factor and an asymptotic expansion for the LR statistic, respectively, when the sample size is large. In this paper we extend the Bartlett correction factor to an elliptical population. The accuracy of our approximations is examined through simulation experiments.