Assuming that the null hypothesis is an equicorrelation matrix and the alternative hypothesis is general, if the null hypothesis cannot be rejected and the estimate of the equicorrelation coefficient is very small, a hypothesis test regarding the mutual independence among variables can be considered. In this paper, we present statistics based on the likelihood ratio principle and a heuristic minimum distance approach for testing the statistical hypothesis of mutual independence versus an equicorrelation structure among multivariate variables, and compare the properties and power of these statistics. Simulation results confirmed that if the correlation coefficient has a positive value under the multivariate normal distribution assumption, the power of the statistics based on the minimum distance is slightly dominant. However, no statistically significant differences were detected between the two methods. The primary advantage of this heuristic approach lies in its distribution-free nature. Unlike traditional parametric tests that rely heavily on the assumption of multivariate normality, the minimum distance statistic provides a reliable assessment even when the underlying data structure is complex.
Yong Chan Jung (Thu,) studied this question.