Heuristic Testing for Independence versus Equicorrelation

When the null hypothesis of equicorrelation structure is not rejected, and in the ensuing estimation process a considerably all common correlation coefficient is resulted, we may naturally need to consider the problem of testing for the mutual independence. The purpose of this paper is to study statistics for testing the hypothesis of mutual independence versus equicorrelation and to investigate the empirical power of those statistics. The proposed statistics are likelihood ratio statistic and ellipsoidal elongation statistic based on eigenvalues of sample correlation matrix. By the simulation results, we can suggest the ellipsoidal elongation statistic as a good test statistic for the case of ρ > 0 under normality.