By Norbert Henze and Mathew D. Penrose.

Suppose there are n independent d-variate random varaibles Xi with common density f, and n independent d-variate random varaibles Yj with common density g. Let Rm,n be the number of edges in the minimal spanning tree with vertices X1,..., Xm, Y1,..., Yn, that connect points from different samples. Friedman and Rafsky conjectured that a test of H0:f=g that rejects H0 for small values of Rm,n should have power against general alternatives. We prove that Rm,n is asymptotically distribution-free under H0, and that the multivariate two-sample test based on Rm,n is universally consistent.

Annals of Statistics 27, 290-298 (1999).