On the Asymptotic Properties of a NonparametrictexL₁/tex-Test Statistic of Homogeneity

We present two simple and explicit procedures for testing homogeneity of two independent multivariate samples of size n. The nonparametric tests are based on the statistic T/sub n/, which is the L/sub 1/ distance between the two empirical distributions restricted to a finite partition. Both tests reject the null hypothesis of homogeneity if T/sub n/ becomes large, i.e., if T/sub n/ exceeds a threshold. We first discuss Chernoff-type large deviation properties of T/sub n/. This results in a distribution-free strong consistent test of homogeneity. Then the asymptotic null distribution of the test statistic is obtained, leading to an asymptotically /spl alpha/-level test procedure.