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On the Multivariate Runs Test
Norbert Henze and Mathew D. Penrose
The Annals of Statistics
Vol. 27, No. 1 (Feb., 1999), pp. 290-298
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/120129
Page Count: 9
You can always find the topics here!Topics: Vertices, Neighborhoods, Mathematical problems, Poisson process, Statistics, Probabilities, Statistical variance, Statism, Density distributions, Topological theorems
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For independent d-variate random variables X1,... ,Xm with common density f and Y1,... ,Yn 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.
The Annals of Statistics © 1999 Institute of Mathematical Statistics