A New Graph-Based Two-Sample Test for Multivariate and Object Data
A New Graph-Based Two-Sample Test for Multivariate and Object Data
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DOI：
10.1080/01621459.2016.1147356
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发表时间：
2017-01-01
影响因子：
3.7
通讯作者：
Friedman, Jerome H.
中科院分区：
文献类型：
--
作者：
Chen, Hao;Friedman, Jerome H.
多变量数据的双样本检验，特别是非欧几里德数据的双样本检验还没有得到很好的研究。本文提出了一种新的检验统计量的基础上，从两个样本的合并观察构建的相似性图。它可以应用于多变量数据和非欧几里德数据，只要可以定义样本空间上的相异性度量，这通常可以由领域专家提供。现有的测试基于相似性图缺乏权力的位置或规模的替代品。新的测试使用了一个以前被忽视的共同模式，并适用于两种类型的替代品。该测试在模拟研究中表现出显著的功率增益。它的渐近置换零分布的推导和证明，以及在有限样本下工作，方便其应用到大型数据集。新的测试说明了两个应用程序：协变量平衡的匹配观察研究的评估，并在不同条件下的网络数据的比较。
Two-sample tests for multivariate data and especially for non-Euclidean data are not well explored. This article presents a novel test statistic based on a similarity graph constructed on the pooled observations from the two samples. It can be applied to multivariate data and non-Euclidean data as long as a dissimilarity measure on the sample space can be defined, which can usually be provided by domain experts. Existing tests based on a similarity graph lack power either for location or for scale alternatives. The new test uses a common pattern that was overlooked previously, and works for both types of alternatives. The test exhibits substantial power gains in simulation studies. Its asymptotic permutation null distribution is derived and shown to work well under finite samples, facilitating its application to large datasets. The new test is illustrated on two applications: The assessment of covariate balance in a matched observational study, and the comparison of network data under different conditions.