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Testing High-Dimensional Nonparametric Behrens-Fisher Problem

MENG Zhen1,2, LI Na1,2, YUAN Ao3   

  1. 1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;2. University of Chinese Academy of Sciences, Beijing 100049, China;3. Department of Biostatistics, Bioinformatics and Biomathematics, Georgetown University, Washington 20057, USA
  • Received:2020-10-12 Revised:2020-11-02 Published:2022-06-20
  • Supported by:
    This research was supported by the National Natural Science Foundation of China under Grant No. 61903312, Huiyan Project for Research on Innovation and Application of Space Science and Technology under Grant No. CD2B65B6.

MENG Zhen, LI Na, YUAN Ao. Testing High-Dimensional Nonparametric Behrens-Fisher Problem[J]. Journal of Systems Science and Complexity, 2022, 35(3): 1098-1115.

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 Rankbased Test (URT) and another is Cauchy Combination Test (CCT). CCT is analogous to the maximumtype 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.
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