A Non-Parametric Test for the Bivariate Two-Sample Location Problem
Kanti V. Mardia · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1967
Summary An unconditional non-parametric test for the bivariate two-sample problem is proposed. The test is shown to possess various desirable properties. We give critical values of the distribution, some approximations and its asymptotic distribution. For the shift type of alternative hypotheses, we show here that U is distributed asymptotically as a non-central chi-square. We have derived its Pitman's asymptotic efficiency relative to Hotelling's T 2 for these alternatives and shown that in the normal case the ARE is ¼π. Suitable examples are constructed to show that the ARE can approach zero and infinity. An extension to the multivariate multi-sample problem is also indicated.