NONPARAMETRIC-TESTS FOR THE MULTIVARIATE MULTISAMPLE 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 ell iptically symmetric distributions. Comparisons are made between the pr oposed statistics and several competitors via Pitman asymptotic relati ve efficiencies and Monte Carlo results. The tests proposed perform be tter than the Lawley-Hotelling generalized T-2 for heavy-tailed distri butions. For normal to light-tailed distributions, the proposed statis tics also perform better than other nonparametric competitors and the proposed analog of the signed-rank test performs better than the Lawle y-Hotelling generalized T-2 for light-tailed distributions.