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Identity tests for high dimensional data using RMT

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  • Wang, Cheng
  • Yang, Jing
  • Miao, Baiqi
  • Cao, Longbing

Abstract

In this work, we redefined two important statistics, the CLRT test [Z. Bai, D. Jiang, J. Yao, S. Zheng, Corrections to LRT on large-dimensional covariance matrix by RMT, The Annals of Statistics 37 (6B) (2009) 3822–3840] and the LW test [O. Ledoit, M. Wolf, Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size, The Annals of Statistics (2002) 1081–1102] on identity tests for high dimensional data using random matrix theories. Compared with existing CLRT and LW tests, the new tests can accommodate data which has unknown means and non-Gaussian distributions. Simulations demonstrate that the new tests have good properties in terms of size and power. What is more, even for Gaussian data, our new tests perform favorably in comparison to existing tests. Finally, we find the CLRT is more sensitive to eigenvalues less than 1 while the LW test has more advantages in relation to detecting eigenvalues larger than 1.

Suggested Citation

  • Wang, Cheng & Yang, Jing & Miao, Baiqi & Cao, Longbing, 2013. "Identity tests for high dimensional data using RMT," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 128-137.
    • Handle: RePEc:eee:jmvana:v:118:y:2013:i:c:p:128-137
    DOI: 10.1016/j.jmva.2013.03.015
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    References listed on IDEAS

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    1. Silverstein, J. W., 1995. "Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 331-339, November.
    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. Silverstein, J. W. & Bai, Z. D., 1995. "On the Empirical Distribution of Eigenvalues of a Class of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 175-192, August.
    5. Schott, James R., 2006. "A high-dimensional test for the equality of the smallest eigenvalues of a covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 827-843, April.
    6. Lin, Zhengyan & Xiang, Yanbiao, 2008. "A hypothesis test for independence of sets of variates in high dimensions," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2939-2946, December.
    7. Pan, Guangming, 2010. "Strong convergence of the empirical distribution of eigenvalues of sample covariance matrices with a perturbation matrix," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1330-1338, July.
    8. Birke, Melanie & Dette, Holger, 2005. "A note on testing the covariance matrix for large dimension," Statistics & Probability Letters, Elsevier, vol. 74(3), pages 281-289, October.
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    Cited by:

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    2. Wang, Cheng, 2014. "Asymptotic power of likelihood ratio tests for high dimensional data," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 184-189.

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