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

Jen Fue Maa, Dennis Keith Pearl, Robert Bartoszyński

Research output: Contribution to journalArticle

43 Citations (Scopus)

Abstract

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
Volume24
Issue number3
DOIs
StatePublished - Jan 1 1996

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Equality
Multivariate Distribution
Univariate
Dimensionality
Multivariate distribution

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Maa, Jen Fue ; Pearl, Dennis Keith ; Bartoszyński, Robert. / Reducing multidimensional two-sample data to one-dimensional interpoint comparisons. In: Annals of Statistics. 1996 ; Vol. 24, No. 3. pp. 1069-1074.
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Reducing multidimensional two-sample data to one-dimensional interpoint comparisons. / Maa, Jen Fue; Pearl, Dennis Keith; Bartoszyński, Robert.

In: Annals of Statistics, Vol. 24, No. 3, 01.01.1996, p. 1069-1074.

Research output: Contribution to journalArticle

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