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A new test for the proportionality of two large-dimensional covariance matrices

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  • Liu, Baisen
  • Xu, Lin
  • Zheng, Shurong
  • Tian, Guo-Liang

Abstract

Let X1,…,Xn1+1∼iidNp(μ1,Σ1) and Y1,…,Yn2+1∼iidNp(μ2,Σ2) be two independent random samples, where p

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:131:y:2014:i:c:p:293-308
    DOI: 10.1016/j.jmva.2014.06.008
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    References listed on IDEAS

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    1. Srivastava, M. S. & Khatri, C. G. & Carter, E. M., 1978. "On monotonicity of the modified likelihood ratio test for the equality of two covariances," Journal of Multivariate Analysis, Elsevier, vol. 8(2), pages 262-267, June.
    2. Christophe Pérignon & Christophe Villa, 2006. "Sources of Time Variation in the Covariance Matrix of Interest Rates," The Journal of Business, University of Chicago Press, vol. 79(3), pages 1535-1550, May.
    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. D. Nel & P. Groenewald, 1993. "A Bayesian approach to the multivariate Behrens-Fisher problem under the assumption of proportional covariance matrices," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 2(1), pages 111-124, December.
    5. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
    6. Schott, James R., 1999. "A test for proportional covariance matrices," Computational Statistics & Data Analysis, Elsevier, vol. 32(2), pages 135-146, December.
    7. 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. Ahmad, Rauf, 2022. "Tests for proportionality of matrices with large dimension," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    2. Tsukuda, Koji & Matsuura, Shun, 2019. "High-dimensional testing for proportional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 412-420.
    3. Xu, Kai & Tian, Yan & He, Daojiang, 2021. "A high dimensional nonparametric test for proportional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    4. 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).
    5. 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).
    6. Tingting Zou & Shurong Zheng & Zhidong Bai & Jianfeng Yao & Hongtu Zhu, 2022. "CLT for linear spectral statistics of large dimensional sample covariance matrices with dependent data," Statistical Papers, Springer, vol. 63(2), pages 605-664, April.

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