An exact distribution-free test comparing two multivariate distributions based on adjacency
An exact distribution-free test comparing two multivariate distributions based on adjacency
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DOI：
10.1111/j.1467-9868.2005.00513.x
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发表时间：
2005-09-01
影响因子：
5.8
通讯作者：
Rosenbaum, PR
中科院分区：
文献类型：
--
作者：
Rosenbaum, PR
提出了一种利用观测值间距离比较两个多元分布的新检验方法。与使用点间距离的早期测试不同，新的测试统计量具有已知的精确分布，并且完全不受分布影响。点间距离用于构造最优的非二部匹配，即将观测值匹配成不相交的对，以最小化对内的总距离。交叉匹配统计量是包含来自第一个分布的一个观测值和来自第二个分布的一个观测值的对的数量。非常不同的分布将显示很少的交叉匹配。当比较具有有限支持的两个离散分布时，测试对所有替代方案都是一致的。该测试应用于一项研究，通过功能性磁共振成像测量两种语言任务期间的大脑活动，将动静脉异常受损的大脑与正常对照进行比较。我们还讨论了另一种完全无分布检验：它对配对进行排序，并对交叉匹配配对的排列求和。
A new test is proposed comparing two multivariate distributions by using distances between observations. Unlike earlier tests using interpoint distances, the new test statistic has a known exact distribution and is exactly distribution free. The interpoint distances are used to construct an optimal non-bipartite matching, i.e. a matching of the observations into disjoint pairs to minimize the total distance within pairs. The cross-match statistic is the number of pairs containing one observation from the first distribution and one from the second. Distributions that are very different will exhibit few cross-matches. When comparing two discrete distributions with finite support, the test is consistent against all alternatives. The test is applied to a study of brain activation measured by functional magnetic resonance imaging during two linguistic tasks, comparing brains that are impaired by arteriovenous abnormalities with normal controls. A second exact distribution-free test is also discussed: it ranks the pairs and sums the ranks of the cross-matched pairs.