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A new test for sphericity of the covariance matrix for high dimensional data

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  • Fisher, Thomas J.
  • Sun, Xiaoqian
  • Gallagher, Colin M.

Abstract

In this paper we propose a new test procedure for sphericity of the covariance matrix when the dimensionality, p, exceeds that of the sample size, N=n+1. Under the assumptions that (A) as p-->[infinity] for i=1,...,16 and (B) p/n-->c [infinity]. Our simulation results show that the new test is comparable to, and in some cases more powerful than, the tests for sphericity in the current literature.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:10:p:2554-2570
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    Cited by:

    1. Gupta, Arjun K. & Bodnar, Taras, 2014. "An exact test about the covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 176-189.
    2. Wang, Zhendong & Xu, Xingzhong, 2021. "Testing high dimensional covariance matrices via posterior Bayes factor," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    3. 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.
    4. 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.
    5. Tian, Xintao & Lu, Yuting & Li, Weiming, 2015. "A robust test for sphericity of high-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 217-227.
    6. Qin, Yingli & Li, Weiming, 2016. "Testing the order of a population spectral distribution for high-dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 75-82.
    7. Wang, Xuanci & Zhang, Bin, 2024. "Target selection in shrinkage estimation of covariance matrix: A structural similarity approach," Statistics & Probability Letters, Elsevier, vol. 208(C).
    8. Zhang, Xiaoxu & Zhao, Ping & Feng, Long, 2022. "Robust sphericity test in the panel data model," Statistics & Probability Letters, Elsevier, vol. 182(C).
    9. Bodnar, Olha & Bodnar, Taras & Parolya, Nestor, 2022. "Recent advances in shrinkage-based high-dimensional inference," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    10. Deepak Nag Ayyala & Santu Ghosh & Daniel F. Linder, 2022. "Covariance matrix testing in high dimension using random projections," Computational Statistics, Springer, vol. 37(3), pages 1111-1141, July.
    11. Mao, Guangyu, 2014. "A note on tests of sphericity and cross-sectional dependence for fixed effects panel model," Economics Letters, Elsevier, vol. 122(2), pages 215-219.
    12. 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.
    13. Zhendong Wang & Xingzhong Xu, 2021. "High-dimensional sphericity test by extended likelihood ratio," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1169-1212, November.
    14. Liu, Baisen & Xu, Lin & Zheng, Shurong & Tian, Guo-Liang, 2014. "A new test for the proportionality of two large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 293-308.
    15. Qian, Manling & Tao, Li & Li, Erqian & Tian, Maozai, 2020. "Hypothesis testing for the identity of high-dimensional covariance matrices," Statistics & Probability Letters, Elsevier, vol. 161(C).
    16. Bodnar, Taras & Dette, Holger & Parolya, Nestor, 2019. "Testing for independence of large dimensional vectors," MPRA Paper 97997, University Library of Munich, Germany, revised May 2019.

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