Eigenprojections and the equality of latent roots of a correlation matrix

In this paper, we consider the inference problem regarding the equality of the q smallest latent roots of a correlation matrix. A statistic, which is a function of the eigenprojection associated with the q smallest latent roots of the sample correlation matrix, is shown to have an asymptotic normal distribution. The expected value of this statistic is the zero vector if, and only if, the q smallest latent roots of the population correlation matrix are equal. This permits the construction of a chi-squared test statistic for the test of the equality of the q smallest latent roots of a population correlation matrix. Simulation results indicate that this test is superior to others currently in use in terms of achieving the nominal significance level for small sample sizes.