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Test on the linear combinations of covariance matrices in high-dimensional data

Author

Listed:
  • Zhidong Bai

    (Northeast Normal University)

  • Jiang Hu

    (Northeast Normal University)

  • Chen Wang

    (University of Hong Kong)

  • Chao Zhang

    (Northeast Normal University)

Abstract

In this paper, we propose a new test on the linear combinations of covariance matrices in high-dimensional data. Our statistic can be applied to many hypothesis tests on covariance matrices. In particular, the test proposed by Li and Chen (Ann Stat 40:908–940, 2012) on the homogeneity of two population covariance matrices is a special case of our test. The results are illustrated by an empirical example in financial portfolio allocation.

Suggested Citation

  • Zhidong Bai & Jiang Hu & Chen Wang & Chao Zhang, 2021. "Test on the linear combinations of covariance matrices in high-dimensional data," Statistical Papers, Springer, vol. 62(2), pages 701-719, April.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:2:d:10.1007_s00362-019-01110-1
    DOI: 10.1007/s00362-019-01110-1
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    References listed on IDEAS

    as
    1. Huiqin Li & Jiang Hu & Zhidong Bai & Yanqing Yin & Kexin Zou, 2017. "Test on the linear combinations of mean vectors in high-dimensional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 188-208, March.
    2. Chen, Songxi, 2012. "Two Sample Tests for High Dimensional Covariance Matrices," MPRA Paper 46026, University Library of Munich, Germany.
    3. Srivastava, Muni S. & Yanagihara, Hirokazu, 2010. "Testing the equality of several covariance matrices with fewer observations than the dimension," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1319-1329, July.
    4. Tony Cai & Weidong Liu & Yin Xia, 2013. "Two-Sample Covariance Matrix Testing and Support Recovery in High-Dimensional and Sparse Settings," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 265-277, March.
    5. 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.
    6. Jiang Hu & Zhidong Bai & Chen Wang & Wei Wang, 2017. "On testing the equality of high dimensional mean vectors with unequal covariance matrices," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(2), pages 365-387, April.
    7. Chao Zhang & Zhidong Bai & Jiang Hu & Chen Wang, 2018. "Multi-sample test for high-dimensional covariance matrices," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(13), pages 3161-3177, July.
    8. Rosa Arboretti & Riccardo Ceccato & Livio Corain & Fabrizio Ronchi & Luigi Salmaso, 2018. "Multivariate small sample tests for two-way designs with applications to industrial statistics," Statistical Papers, Springer, vol. 59(4), pages 1483-1503, December.
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    Cited by:

    1. Jin-Ting Zhang & Bu Zhou & Jia Guo, 2022. "Testing high-dimensional mean vector with applications," Statistical Papers, Springer, vol. 63(4), pages 1105-1137, August.
    2. Jianghao Li & Shizhe Hong & Zhenzhen Niu & Zhidong Bai, 2025. "Test for high-dimensional linear hypothesis of mean vectors via random integration," Statistical Papers, Springer, vol. 66(1), pages 1-34, January.

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