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Testing High-Dimensional Nonparametric Behrens-Fisher Problem

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Abstract

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.

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Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Zhen Meng & Na Li

  2. University of Chinese Academy of Sciences, Beijing, 100049, China

    Zhen Meng & Na Li

  3. Department of Biostatistics, Bioinformatics and Biomathematics, Georgetown University, Washington, 20057, USA

    Ao Yuan

Authors
  1. Zhen Meng
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  2. Na Li
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  3. Ao Yuan
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Corresponding author

Correspondence to Na Li.

Additional information

This paper was supported by Beijing Natural Science Foundation under Grant No. Z180006 and the National Nature Science Foundation of China under Grant No. 11722113.

This paper was recommended for publication by Editor LI Qizhai.

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Meng, Z., Li, N. & Yuan, A. Testing High-Dimensional Nonparametric Behrens-Fisher Problem. J Syst Sci Complex 35, 1098–1115 (2022). https://doi.org/10.1007/s11424-021-0257-3

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  • DOI: https://doi.org/10.1007/s11424-021-0257-3

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