Nonparametric tests for the multivariate multi-sample location problem

Nonparametric tests for the multi-sample multivariate location problem are proposed which extend the, two-sample multivariate rank tests by Randles and Peters (1990) to the multi-sample setting. The asymptotic distributions of the proposed statistics under the null hypothesis and under certain contiguous alternatives are obtained for a class of elliptically symmetric distributions. Comparisons are made between the proposed statistics and several competitors via Pitman asymptotic relative efficiencies and Monte Carlo results. The tests proposed perform better than the Lawley-Hotelling generalized T-2 for heavy-tailed distributions. For normal to light-tailed distributions, the proposed statistics also perform better than other nonparametric competitors and the proposed analog of the signed-rank test performs better than the Lawley-Hotelling generalized T-2 for light-tailed distributions.