A Two-Sample Test for Equality of Means in High Dimension.
A Two-Sample Test for Equality of Means in High Dimension.
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DOI：
10.1080/01621459.2014.934826
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发表时间：
2015-06-01
影响因子：
3.7
通讯作者：
Lahiri SN
中科院分区：
文献类型：
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作者：
Gregory KB;Carroll RJ;Baladandayuthapani V;Lahiri SN
我们开发了一个检验统计量，用于在“大p小n”设置中检验两个总体平均向量的相等性。这种检验必须克服样本协方差矩阵的秩不足，这就打破了经典的Hotelling T2检验。所提出的程序，称为广义分量检验，通过假设p个分量承认逻辑顺序，使分量之间的依赖关系与它们的位移有关，从而避免了对协方差矩阵的完全估计。结果表明，在ARMA和远程依赖结构下，该测试与最近开发的其他方法具有竞争力，并且在重尾数据方面具有优越的性能。该测试不假设两个群体之间的协方差矩阵相等，对成分方差的异方差具有鲁棒性，并且需要很少的计算时间，这使得它可以在非常大的p设置中使用。对小鼠心肌中线粒体钙浓度随时间的变化和来自癌症基因组图谱的胶质母细胞瘤多形态数据集的拷贝数变化进行了分析，以说明该测试。
We develop a test statistic for testing the equality of two population mean vectors in the “large-p-small-n” setting. Such a test must surmount the rank-deficiency of the sample covariance matrix, which breaks down the classic Hotelling T2 test. The proposed procedure, called the generalized component test, avoids full estimation of the covariance matrix by assuming that the p components admit a logical ordering such that the dependence between components is related to their displacement. The test is shown to be competitive with other recently developed methods under ARMA and long-range dependence structures and to achieve superior power for heavy-tailed data. The test does not assume equality of covariance matrices between the two populations, is robust to heteroscedasticity in the component variances, and requires very little computation time, which allows its use in settings with very large p. An analysis of mitochondrial calcium concentration in mouse cardiac muscles over time and of copy number variations in a glioblastoma multiforme data set from The Cancer Genome Atlas are carried out to illustrate the test.