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Testing proportionality of two large-dimensional covariance matrices

Author

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  • Xu, Lin
  • Liu, Baisen
  • Zheng, Shurong
  • Bao, Shaokun

Abstract

Testing the proportionality of two large-dimensional covariance matrices is studied. Based on modern random matrix theory, a pseudo-likelihood ratio statistic is proposed and its asymptotic normality is proved as the dimension and sample sizes tend to infinity proportionally.

Suggested Citation

  • Xu, Lin & Liu, Baisen & Zheng, Shurong & Bao, Shaokun, 2014. "Testing proportionality of two large-dimensional covariance matrices," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 43-55.
    • Handle: RePEc:eee:csdana:v:78:y:2014:i:c:p:43-55
    DOI: 10.1016/j.csda.2014.03.014
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    References listed on IDEAS

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    1. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
    2. Schott, James R., 1999. "A test for proportional covariance matrices," Computational Statistics & Data Analysis, Elsevier, vol. 32(2), pages 135-146, December.
    3. Flury, Bernhard K., 1986. "Proportionality of k covariance matrices," Statistics & Probability Letters, Elsevier, vol. 4(1), pages 29-33, January.
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    Cited by:

    1. Xu, Kai & Tian, Yan & He, Daojiang, 2021. "A high dimensional nonparametric test for proportional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    2. Cheng, Guanghui & Liu, Baisen & Tian, Guoliang & Zheng, Shurong, 2020. "Testing proportionality of two high-dimensional covariance matrices," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    3. Tsukuda, Koji & Matsuura, Shun, 2019. "High-dimensional testing for proportional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 412-420.
    4. Tsukuda, Koji & Matsuura, Shun, 2021. "Limit theorem associated with Wishart matrices with application to hypothesis testing for common principal components," Journal of Multivariate Analysis, Elsevier, vol. 186(C).

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