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A simultaneous testing of the mean vector and the covariance matrix among two populations for high-dimensional data

Author

Listed:
  • Masashi Hyodo

    (Osaka Prefecture University)

  • Takahiro Nishiyama

    (Senshu University)

Abstract

In this article, we propose an $$L^2$$ L 2 -norm-based test for simultaneous testing of the mean vector and the covariance matrix under high-dimensional non-normal populations. To construct this, we derive an asymptotic distribution of a test statistic based on both differences mean vectors and covariance matrices. We also investigate the asymptotic sizes and powers of the proposed test using this result. Finally, we study the finite sample and dimension performance of this test via Monte Carlo simulations.

Suggested Citation

  • Masashi Hyodo & Takahiro Nishiyama, 2018. "A simultaneous testing of the mean vector and the covariance matrix among two populations for high-dimensional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 680-699, September.
    • Handle: RePEc:spr:testjl:v:27:y:2018:i:3:d:10.1007_s11749-017-0567-x
    DOI: 10.1007/s11749-017-0567-x
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    References listed on IDEAS

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    1. Chen, Songxi, 2012. "Two Sample Tests for High Dimensional Covariance Matrices," MPRA Paper 46026, University Library of Munich, Germany.
    2. 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.
    3. 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.
    4. Dudoit S. & Fridlyand J. & Speed T. P, 2002. "Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 77-87, March.
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    Cited by:

    1. Mingxiang Cao & Yuanjing He, 2022. "A high-dimensional test on linear hypothesis of means under a low-dimensional factor model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(5), pages 557-572, July.

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