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An exact test about the covariance matrix

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  • Gupta, Arjun K.
  • Bodnar, Taras

Abstract

In the present paper, we propose an exact test on the structure of the covariance matrix. In its development the properties of the Wishart distribution are used. Unlike the classical likelihood-ratio type tests and the tests based on the empirical distance, whose statistics depend on the total variance and the generalized variance only, the proposed approach provides more information about the changes in the covariance matrix. Via an extensive simulation study the new approach is compared with the existent asymptotic tests.

Suggested Citation

  • Gupta, Arjun K. & Bodnar, Taras, 2014. "An exact test about the covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 176-189.
    • Handle: RePEc:eee:jmvana:v:125:y:2014:i:c:p:176-189
    DOI: 10.1016/j.jmva.2013.12.007
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    References listed on IDEAS

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    1. Bodnar, Taras & Okhrin, Yarema, 2008. "Properties of the singular, inverse and generalized inverse partitioned Wishart distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2389-2405, November.
    2. Fisher, Thomas J. & Sun, Xiaoqian & Gallagher, Colin M., 2010. "A new test for sphericity of the covariance matrix for high dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2554-2570, November.
    3. Arjun Gupta & Jin Xu, 2006. "On Some Tests of the Covariance Matrix Under General Conditions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(1), pages 101-114, March.
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    Cited by:

    1. Butucea, Cristina & Zgheib, Rania, 2016. "Sharp minimax tests for large Toeplitz covariance matrices with repeated observations," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 164-176.
    2. Bodnar, Taras & Mazur, Stepan & Ngailo, Edward & Parolya, Nestor, 2017. "Discriminant analysis in small and large dimensions," Working Papers 2017:6, Örebro University, School of Business.
    3. Bodnar, Taras & Reiß, Markus, 2016. "Exact and asymptotic tests on a factor model in low and large dimensions with applications," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 125-151.
    4. Bodnar, Olha & Bodnar, Taras & Parolya, Nestor, 2022. "Recent advances in shrinkage-based high-dimensional inference," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

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