ON THE MULTIVARIATE RUNS TEST
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
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
is asymptotically distribution-free under
and that the multivariate two-sample test based on
is universally consistent.
Annals of Statistics 27, 290-298 (1999).