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

• 成果类型: Article
• 署名作者: Maa, JF; Pearl, DK; Bartoszynski, R
• 署名单位: University System of Ohio; Ohio State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1996
• 页码: 1069-1074
• 关键词: multivariate

摘要

The most popular technique for reducing the dimensionality in comparing two multidimensional samples of X similar to F and Y similar to 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(X(1),X(2)) =(L) h(Y-1,Y-2)) and ii) the equality of these with the distribution of between sample comparisons ((h(X(1),X(2)) =(L) h(X(3),Y-3)) is equivalent to the equality of the multivariate distributions (F = G).