Testing High-Dimensional Nonparametric Behrens-Fisher Problem

MENG Zhen, LI Na, YUAN Ao

系统科学与复杂性(英文) ›› 2022, Vol. 35 ›› Issue (3) : 1098-1115.

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系统科学与复杂性(英文) ›› 2022, Vol. 35 ›› Issue (3) : 1098-1115. DOI: 10.1007/s11424-021-0257-3

Testing High-Dimensional Nonparametric Behrens-Fisher Problem

    MENG Zhen1,2, LI Na1,2, YUAN Ao3
作者信息 +

Testing High-Dimensional Nonparametric Behrens-Fisher Problem

    MENG Zhen1,2, LI Na1,2, YUAN Ao3
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文章历史 +

摘要

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.

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 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.

关键词

Cauchy combination test / nonparametric Behrens-Fisher problem / rank-based test / Ustatistic

Key words

Cauchy combination test / nonparametric Behrens-Fisher problem / rank-based test / Ustatistic

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MENG Zhen, LI Na, YUAN Ao. Testing High-Dimensional Nonparametric Behrens-Fisher Problem. 系统科学与复杂性(英文), 2022, 35(3): 1098-1115 https://doi.org/10.1007/s11424-021-0257-3
MENG Zhen, LI Na, YUAN Ao. Testing High-Dimensional Nonparametric Behrens-Fisher Problem. Journal of Systems Science and Complexity, 2022, 35(3): 1098-1115 https://doi.org/10.1007/s11424-021-0257-3

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基金

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.
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