Reducing multidimensional two-sample data to one-dimensional interpoint comparisons
Reducing multidimensional two-sample data to one-dimensional interpoint comparisons
复制标题
将多维二维样本数据简化为一维点间比较
DOI：
10.1214/aos/1032526956
复制
发表时间：
1996
影响因子：
4.5
通讯作者：
R. Bartoszynski
中科院分区：
文献类型：
--
作者：
J. Maa;D. Pearl;R. Bartoszynski
在比较两个多维样本X F和Y G时，最流行的降维技术是基于单变量函数h（例如点间距离）分析点间比较的分布。我们提供了一个理论基础，这种技术，通过表明，有两个i）平等的分布内的样本比较，（h（X 1，X 2）= L h（Y1，Y2））和ii）这些与样本间比较分布的相等性（（h（X1，X2）= Lh（X3，Y3））等价于多元分布（F = G）的相等性。
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(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).