Testing the equality for two-sample means with high dimensional distributions is a fundamental problem in statistics. In the past two decades, many efforts have been devoted to comparing the mean vectors of two populations. Many existing tests rely on naive diagonal or trace estimators of the covariance matrix, ignoring the dependence structure between variables. To make more use of the dependence structure, a new nonparametric test based on random selections is proposed to test the population mean vector of nonnormal high-dimensional multivariate data. This makes more efficient use of the covariance structure to deal with dependent variables. The asymptotic null distribution of the proposed test is standard normal, regardless of the parent distributions of the random samples and the relations between data dimensions and sample sizes. Extensive simulations show that the power performance of the proposed test is encouraging compared with some existing methods.

测试具有高维分布的两个样本均值的相等性是统计学中的一个基本问题。在过去的二十年中，已经进行了许多努力来比较两个总体的均值向量。许多现有测试依赖于协方差矩阵的朴素对角线或轨迹估计量，而忽略了变量之间的依存关系。为了充分利用依存结构，提出了一种新的基于随机选择的非参数检验来检验非正态高维多元数据的总体均值向量。这样可以更有效地利用协方差结构来处理因变量。所提出的测试的渐近零分布是标准正态的，而与随机样本的父分布以及数据维数和样本大小之间的关系无关。