An overview of tests on high-dimensional means
An overview of tests on high-dimensional means
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DOI：
10.1016/j.jmva.2021.104813
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发表时间：
2021-09
期刊：
影响因子：
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通讯作者：
Yuan Huang;Changcheng Li;Runze Li;Songshan Yang
中科院分区：
文献类型：
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作者：
Yuan Huang;Changcheng Li;Runze Li;Songshan Yang
高维测试方法在科学研究中有着广泛的应用。例如，在遗传学研究中，测试对照组和治疗组之间的基因表达是否存在差异是非常有意义的。这可以用公式表示为双样本均值检验问题。然而，当样本容量小于数据维数时，由于样本协方差矩阵的奇异性，两样本均值问题的Hotelling T2检验统计量不再是很好的定义。在过去的二十年里，高维均值检验问题在文献中得到了相当大的关注。本文对文献中的现有测试程序进行了选择性概述。我们专注于测试程序的动机，如何构建检验统计量和连接的见解，以及不同方法的比较。
Testing high-dimensional means has many applications in scientific research. For instance, it is of great interest to test whether there is a difference of gene expressions between control and treatment groups in genetic studies. This can be formulated as a two-sample mean testing problem. However, the Hotelling T 2 test statistic for the two-sample mean problem is no longer well defined due to singularity of the sample covariance matrix when the sample size is less than the dimension of data. Over the last two decades, the high-dimensional mean testing problem has received considerable attentions in the literature. This paper provides a selective overview of existing testing procedures in the literature. We focus on the motivation of the testing procedures, the insights into how to construct the test statistics and the connections, and comparisons of different methods.