Testing equality of mean vectors is a very commonly used criterion when comparing two multivariate random variables. Traditional tests such as Hotelling's $T^2$ become either unusable or output small power when the number of variables is greater than the combined sample size. A novel method is proposed using both prepivoting and Edgeworth expansion for testing the equality of two population mean vectors in a “large p, small n” setting. The asymptotic null distribution of the test statistic is derived and it is shown that the power of suggested test converges to one under certain alternatives when both n and p increase to infinity. Finite sample performance of the proposed test statistic is compared with other recently developed tests designed to also handle the “large p, small n” situation through simulations. The proposed test achieves competitive rates for both type I error rate and power. The usefulness of suggested test is illustrated by applications to two microarray gene expression data sets.

在比较两个多元随机变量时，测试均值向量的相等性是一个非常常用的标准。传统测试，例如 Hotelling 的${吨}^2$当变量数量大于合并样本大小时，变得不可用或输出较小的功效。提出了一种新方法，使用预透视和 Edgeworth 扩展来测试“大p，小 n”设置中两个总体均值向量的相等性。推导出检验统计量的渐近零分布，并表明当n和p 都增加到无穷大时，建议检验的功效在某些替代方案下收敛到 1 。将提议的测试统计量的有限样本性能与其他最近开发的测试进行比较，这些测试旨在也处理“大p，小n”情况通过模拟。建议的测试在 I 类错误率和功率方面都达到了具有竞争力的比率。通过对两个微阵列基因表达数据集的应用说明了建议测试的有用性。