Abstract: We introduce a novel projection mean variance (PMV) measure to construct a nonparametric test for the multisample hypothesis of equal distributions for univariate or multivariate responses. The proposed PMV measure generalizes the mean variance index using the projection technique. We obtain the theoretical properties of the PMV measure and its empirical counterpart. The PMV measure yields an analogous variance component decomposition. Using this decomposition, an ANOVA F statistic is derived to test the multisample problem. The proposed test is statistically consistent against the general alternatives and robust to heavytailed data. The test is free of tuning parameters and does not require moment conditions on the response. Our simulation results demonstrate that the PMV test has higher power than the classical Wilks-type methods and DISCO test, especially when the dimension of the response is relatively large or the moment conditions required by the DISCO test are violated. We further illustrate our method using empirical analyses of two real data sets.

Key words and phrases: Independence test, multivariate multisample problem, nonparametric ANOVA extension, nonparametric tests, projection.