A NON-PARAMETRIC METHOD TO TEST EQUALITY OF INTERMEDIATE LATENT ROOTS OF TWO POPULATIONS IN A PRINCIPAL COMPONENT ANALYSIS

Abstract

We propose a nonparametric criterion to test the hypothesis that the j-th largest roots of two populations are equal, in Section 2. This testing procedure is distribution free, and in Section 3 and 4 we show that it is reliable when the sample sizes increase and the population latent roots are separate, under the multivariate normal distribution. We suggest which sample sizes are necessary to rely on the above test.