TESTING FOR EQUAL DISTRIBUTIONS IN HIGH DIMENSION
TESTING FOR EQUAL DISTRIBUTIONS IN HIGH DIMENSION
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发表时间：
2004
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通讯作者：
G. Székely;Maria L. Rizzo
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作者：
G. Székely;Maria L. Rizzo
提出了一种基于样本元素间欧氏距离的两个或多个多元分布相等性的非参数检验方法。从基本的理论结果中可以得出几个用于比较多变量分布的一致性检验。发展了多样本问题的检验方法，并应用于检验均匀分布的复合假设，当分布不是特定分布时。所提出的检验方法对所有具有有限二阶矩的固定备选方案(不一定是连续的)普遍一致。该检验是通过对混合样本进行条件处理来实现的，以获得近似排列检验，该检验是无分布的。我们的蒙特卡罗能力研究表明，新的测试可能比基于最近邻的测试对几类备选方案更敏感，并且在高维方面表现得特别好。我们的测试过程的计算复杂性与样本总体的维度和数量无关。该测试应用于高维问题，测试来自癌症样本的微阵列数据。
We propose a new nonparametric test for equality of two or more multivariate distributions based on Euclidean distance between sample elements. Several consistent tests for comparing multivariate distributions can be developed from the underlying theoretical results. The test procedure for the multisample problem is developed and applied for testing the composite hypothesis of equal distributions, when distributions are unspecified. The proposed test is universally consistent against all fixed alternatives (not necessarily continuous) with finite second moments. The test is implemented by conditioning on the pooled sample to obtain an approximate permutation test, which is distribution free. Our Monte Carlo power study suggests that the new test may be much more sensitive than tests based on nearest neighbors against several classes of alternatives, and performs particularly well in high dimension. Computational complexity of our test procedure is independent of dimension and number of populations sampled. The test is applied in a high dimensional problem, testing microarray data from cancer samples.