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A Jarque-Bera test for sphericity of a large-dimensional covariance matrix

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  • Glombek, Konstantin

Abstract

This article provides a new test for sphericity of the covariance matrix of a d-dimensional multinormal population X ∼ Nd(µ,Σ). This test is applicable if the sample size, n + 1, and d both go to infinity while d/n → y ∈ (0,∞), provided that the limits of tr(Σk)/d, k = 1,...,8, are finite. The main idea of this test is to check whether the empirical eigenvalue distribution of a suitably standardized sample covariance matrix obeys the semicircle law. Due to similarities of the semicircle law to the normal distribution, the proposed test statistic is of the type of the Jarque-Bera test statistic. Simulation results show that the new sphericity test outperforms the tests from the current literature for certain local alternatives if y is small.

Suggested Citation

  • Glombek, Konstantin, 2013. "A Jarque-Bera test for sphericity of a large-dimensional covariance matrix," Discussion Papers in Econometrics and Statistics 1/13, University of Cologne, Institute of Econometrics and Statistics.
    • Handle: RePEc:zbw:ucdpse:113
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    References listed on IDEAS

    as
    1. Srivastava, Muni S. & Kollo, Tõnu & von Rosen, Dietrich, 2011. "Some tests for the covariance matrix with fewer observations than the dimension under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1090-1103, July.
    2. Chen, Song Xi & Zhang, Li-Xin & Zhong, Ping-Shou, 2010. "Tests for High-Dimensional Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 810-819.
    3. 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.
    4. Yin, Y. Q., 1986. "Limiting spectral distribution for a class of random matrices," Journal of Multivariate Analysis, Elsevier, vol. 20(1), pages 50-68, October.
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    More about this item

    Keywords

    Test for covariance matrix; High-dimensional data; Spectral distribution; Semicircle law; Free cumulant; Jarque-Bera test;
    All these keywords.

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