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.

MENG Zhen;LI Na;YUAN Ao

Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China;Univer-sity of Chinese Academy of Sciences,Beijing 100049,China;Department of Biostatistics,Bioinformatics and Biomathematics,Georgetown University,Washington 20057,USA

系统科学与复杂性学报（英文版）

[1]MENG Zhen;LI Na;YUAN Ao-.Testing High-Dimensional Nonparametric Behrens-Fisher Problem)[J].系统科学与复杂性学报（英文版）,2022(03):1098-1115

Behrens

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