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A simpler spatial-sign-based two-sample test for high-dimensional data

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  • Li, Yang
  • Wang, Zhaojun
  • Zou, Changliang

Abstract

This article concerns the tests for the equality of two location parameters when the data dimension is larger than the sample size. Existing spatial-sign-based procedures are not robust with respect to high dimensionality, producing tests with the type-I error rates that are much larger than the nominal levels. We develop a correction that makes the sign-based tests applicable for high-dimensional data, allowing the dimensionality to increase as the square of the sample size. We show that the proposed test statistic is asymptotically normal under elliptical distributions and demonstrate that it has good size and power in a wide range of settings by simulation.

Suggested Citation

  • Li, Yang & Wang, Zhaojun & Zou, Changliang, 2016. "A simpler spatial-sign-based two-sample test for high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 192-198.
    • Handle: RePEc:eee:jmvana:v:149:y:2016:i:c:p:192-198
    DOI: 10.1016/j.jmva.2016.04.004
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    References listed on IDEAS

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    1. Thomas P. Hettmansperger, 2002. "A practical affine equivariant multivariate median," Biometrika, Biometrika Trust, vol. 89(4), pages 851-860, December.
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    3. Chen, Song Xi & Qin, Yingli, 2010. "A Two Sample Test for High Dimensional Data with Applications to Gene-set Testing," MPRA Paper 59642, University Library of Munich, Germany.
    4. Karl Bruce Gregory & Raymond J. Carroll & Veerabhadran Baladandayuthapani & Soumendra N. Lahiri, 2015. "A Two-Sample Test for Equality of Means in High Dimension," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 837-849, June.
    5. Muni S. Srivastava & Hirokazu Yanagihara & Tatsuya Kubokawa, 2014. "Tests for Covariance Matrices in High Dimension with Less Sample Size," CIRJE F-Series CIRJE-F-933, CIRJE, Faculty of Economics, University of Tokyo.
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    Cited by:

    1. 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).
    2. Zhang, Jin-Ting & Zhu, Tianming, 2022. "A new normal reference test for linear hypothesis testing in high-dimensional heteroscedastic one-way MANOVA," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    3. 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).
    4. Pini, Alessia & Stamm, Aymeric & Vantini, Simone, 2018. "Hotelling’s T2 in separable Hilbert spaces," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 284-305.

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