Abstract

In this study, the test statistics for one-sided and two-sided multivariate hypotheses to the high-dimensional two-sample problem with one unknown covariance matrix were proposed. The tests were developed based on the idea of keeping as much information as possible from the pooled sample covariance matrix by arranging the blocks along its diagonal. The asymptotic distributions of the test statistics were derived under the null hypothesis. The performance of the proposed tests were evaluated on both equal and unequal sample sizes via a simulation study. The simulated results showed that the proposed tests performed well for both equal and unequal sample sizes. An illustration of the proposed tests was carried out using a dataset of prostate cancer microarray.

摘要

在这项研究中，针对具有一个未知协方差矩阵的高维双样本问题，提出了单边和双边多元假设的检验统计量。测试的开发基于通过沿其对角线排列块来从合并样本协方差矩阵中保留尽可能多的信息的想法。检验统计量的渐近分布是在原假设下得出的。拟议测试的性能通过模拟研究在相等和不相等的样本量上进行了评估。模拟结果表明，所提出的测试对于相等和不相等的样本量都表现良好。使用前列腺癌微阵列的数据集对所提出的测试进行了说明。