Open Access
June 1996 Reducing multidimensional two-sample data to one-dimensional interpoint comparisons
Jen-Fue Maa, Dennis K. Pearl, Robert Bartoszyński
Ann. Statist. 24(3): 1069-1074 (June 1996). DOI: 10.1214/aos/1032526956


The most popular technique for reducing the dimensionality in comparing two multidimensional samples of $\mathbf{X} \sim F$ and $\mathbf{Y}\sim G$ is to analyze distributions of interpoint comparisons based on a univariate function h (e.g. the interpoint distances). We provide a theoretical foundation for this technique, by showing that having both i) the equality of the distributions of within sample comparisons $(h(\mathbf{X}_1, \mathbf{X}_2) =_L h(\mathbf{Y}_1, \mathbf{Y}_2))$ and ii) the equality of these with the distribution of between sample comparisons $((h(\mathbf{X}_1, \mathbf{X}_2) =_L h(\mathbf{X}_3, \mathbf{Y}_3))$ is equivalent to the equality of the multivariate distributions $(F = G)$.


Download Citation

Jen-Fue Maa. Dennis K. Pearl. Robert Bartoszyński. "Reducing multidimensional two-sample data to one-dimensional interpoint comparisons." Ann. Statist. 24 (3) 1069 - 1074, June 1996.


Published: June 1996
First available in Project Euclid: 20 September 2002

zbMATH: 0862.62047
MathSciNet: MR1401837
Digital Object Identifier: 10.1214/aos/1032526956

Primary: 62H05

Keywords: Characterization of distributional equality , distances , multivariate

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 3 • June 1996
Back to Top