A STATISTIC FOR TESTING THE EQUALITY OF EIGENVALUE OF COVARIANCE MATRIX ON MULTIPOPULATION

A test statistic for the equality of the j-th largest eigenvalues of the covariance matrix in a multipopulation is proposed. Asymptotic distribution of the statistic is derived under the normal population when the sample sizes are equal. By simulation studies, we investigate the power of a test using the suggested statistic for normal, contaminated normal and skew normal populations, and compare it with two nonparametric tests.