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Multivariate-Sign-Based High-Dimensional Tests for the Two-Sample Location Problem

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  • Long Feng
  • Changliang Zou
  • Zhaojun Wang

Abstract

This article concerns tests for the two-sample location problem when data dimension is larger than the sample size. Existing multivariate-sign-based procedures are not robust against high dimensionality, producing tests with Type I error rates far away from nominal levels. This is mainly due to the biases from estimating location parameters. We propose a novel test to overcome this issue by using the “leave-one-out” idea. The proposed test statistic is scalar-invariant and thus is particularly useful when different components have different scales in high-dimensional data. Asymptotic properties of the test statistic are studied. Compared with other existing approaches, simulation studies show that the proposed method behaves well in terms of sizes and power. Supplementary materials for this article are available online.

Suggested Citation

  • Long Feng & Changliang Zou & Zhaojun Wang, 2016. "Multivariate-Sign-Based High-Dimensional Tests for the Two-Sample Location Problem," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 721-735, April.
    • Handle: RePEc:taf:jnlasa:v:111:y:2016:i:514:p:721-735
    DOI: 10.1080/01621459.2015.1035380
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    Cited by:

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    2. Feng, Long & Zhang, Xiaoxu & Liu, Binghui, 2020. "A high-dimensional spatial rank test for two-sample location problems," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    3. Li, Weiming & Xu, Yangchang, 2022. "Asymptotic properties of high-dimensional spatial median in elliptical distributions with application," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    4. Huang, Yuan & Li, Changcheng & Li, Runze & Yang, Songshan, 2022. "An overview of tests on high-dimensional means," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    5. Paul, Biplab & De, Shyamal K. & Ghosh, Anil K., 2022. "Some clustering-based exact distribution-free k-sample tests applicable to high dimension, low sample size data," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    6. Shu, Lei & Chen, Yu & Zhang, Weiping & Wang, Xueqin, 2022. "Spatial rank-based high-dimensional change point detection via random integration," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    7. Feng, Long & Zhang, Xiaoxu & Liu, Binghui, 2020. "Multivariate tests of independence and their application in correlation analysis between financial markets," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    8. M. Rauf Ahmad, 2019. "A unified approach to testing mean vectors with large dimensions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(4), pages 593-618, December.
    9. Harrar, Solomon W. & Kong, Xiaoli, 2022. "Recent developments in high-dimensional inference for multivariate data: Parametric, semiparametric and nonparametric approaches," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

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