For high-dimensional nonparametric Behrens-Fisher problem in which the data dimension is larger than the sample size, the authors propose two test statistics in which one is U-statistic Rank-based Test (URT) and another is Cauchy Combination Test (CCT). CCT is analogous to the maximum-type test, while URT takes into account the sum of squares of differences of ranked samples in different dimensions, which is free of shapes of distributions and robust to outliers. The asymptotic distribution of URT is derived and the closed form for calculating the statistical significance of CCT is given. Extensive simulation studies are conducted to evaluate the finite sample power performance of the statistics by comparing with the existing method. The simulation results show that our URT is robust and powerful method, meanwhile, its practicability and effectiveness can be illustrated by an application to the gene expression data.

对于数据维数大于样本量的高维非参数Behrens-Fisher问题，作者提出了两种检验统计量，一种是U-statistic Rank-based Test (URT)，另一种是Cauchy Combination Test (CCT) . CCT类似于最大型检验，而URT考虑的是不同维度排序样本的差值的平方和，不受分布形状的影响，对异常值具有鲁棒性。推导了URT的渐近分布，并给出了计算CCT统计显着性的封闭形式。通过与现有方法进行比较，进行了广泛的模拟研究以评估统计量的有限样本功效性能。仿真结果表明，我们的 URT 是一种鲁棒且强大的方法，同时，