Reducing multidimensional two-sample data to one-dimensional interpoint comparisons

Jen Fue Maa, Dennis K. Pearl, Robert Bartoszyński

Research output: Contribution to journalArticlepeer-review

61 Scopus citations


The most popular technique for reducing the dimensionality in comparing two multidimensional samples of X ∼ F and Y ∼ 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(X1,X2) = h(Y1,Y2)) and ii) the equality of these with the distribution of between sample comparisons ((h(X1,X2) = h(X3,Y3)) is equivalent to the equality of the multivariate distributions (F = G).

Original languageEnglish (US)
Pages (from-to)1069-1074
Number of pages6
JournalAnnals of Statistics
Issue number3
StatePublished - Jun 1996

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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