Abstract

Two-sample tests for multivariate data and non-Euclidean data are widely used in many fields.  We study a nonparametric testing procedure that utilizes graphs representing the similarity among observations.  It can be applied to any data types as long as an informative similarity measure on the sample space can be defined.  Existing tests based on a similarity graph lack power either for location or for scale alternatives. A new test is proposed that utilizes a common pattern overlooked previously, and it works for both types of alternatives.  The test exhibits substantial power gains in simulation studies. Its asymptotic permutation null distribution is derived and shown to work well under finite samples, facilitating its application to large data sets.  Another new test statistic will also be discussed that addresses the problem of the classic test of the type under unequal sample sizes.  Both tests are illustrated on an application of comparing networks under different conditions.