# 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 language English (US) 1069-1074 6 Annals of Statistics 24 3 https://doi.org/10.1214/aos/1032526956 Published - Jan 1 1996

### Fingerprint

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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