Robust two-sample test of high-dimensional mean vectors under dependence
Robust two-sample test of high-dimensional mean vectors under dependence
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DOI：
10.1016/j.jmva.2018.09.013
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Wei Wang;N. Lin;Xiang Tang
中科院分区：
文献类型：
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作者：
Wei Wang;N. Lin;Xiang Tang
现代多变量分析中的一个基本问题是在维数p随样本大小n增加的情况下检验两个均值向量的相等性。本文提出了一种稳健的两样本测试高维数据对稀疏和强的替代品，其中的人口的平均向量的差异只有几个维度，但差异的幅度是大的。该检验基于截尾均值和稳健精度矩阵估计量。建立了截尾均值的渐近联合分布，并证明了该检验统计量在极限下服从Gumbel分布。模拟研究表明，所提出的测试的数值性能是可比的非鲁棒性测试未污染的数据。对于单元格污染数据，它优于非稳健性检验。一个例子涉及阿尔茨海默病数据集中的生物标志物识别。
A basic problem in modern multivariate analysis is testing the equality of two mean vectors in settings where the dimension p increases with the sample size n. This paper proposes a robust two-sample test for high-dimensional data against sparse and strong alternatives, in which the mean vectors of the populations differ in only a few dimensions, but the magnitude of the differences is large. The test is based on trimmed means and robust precision matrix estimators. The asymptotic joint distribution of the trimmed means is established, and the proposed test statistic is shown to have a Gumbel distribution in the limit. Simulation studies suggest that the numerical performance of the proposed test is comparable to that of non-robust tests for uncontaminated data. For cell-wise contaminated data, it outperforms non-robust tests. An illustration involves biomarker identification in an Alzheimer’s disease dataset.