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Tests for proportionality of matrices with large dimension

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  • Ahmad, Rauf

Abstract

A test for proportionality of two covariance matrices with large dimension, possibly larger than the sample size, is proposed. The test statistic is simple, computationally efficient, and can be used for a large class of multivariate distributions including normality. The properties of the statistic, including asymptotic distribution, are given under high-dimensional set up. Through simulations, the statistic is shown to perform accurately, and outperform its recent competitors, constructed on the basis of similar principles. An extension to the multi-sample case is given.

Suggested Citation

  • Ahmad, Rauf, 2022. "Tests for proportionality of matrices with large dimension," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:jmvana:v:189:y:2022:i:c:s0047259x21001433
    DOI: 10.1016/j.jmva.2021.104865
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    References listed on IDEAS

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    1. Tsukuda, Koji & Matsuura, Shun, 2019. "High-dimensional testing for proportional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 412-420.
    2. 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.
    3. Stefan Fremdt & Josef G. Steinebach & Lajos Horváth & Piotr Kokoszka, 2013. "Testing the Equality of Covariance Operators in Functional Samples," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(1), pages 138-152, March.
    4. Schott, James R., 1999. "A test for proportional covariance matrices," Computational Statistics & Data Analysis, Elsevier, vol. 32(2), pages 135-146, December.
    5. Rauf Ahmad, M., 2019. "A significance test of the RV coefficient in high dimensions," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 116-130.
    6. Graciela Boente & Daniela Rodriguez & Mariela Sued, 2018. "Testing equality between several populations covariance operators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(4), pages 919-950, August.
    7. M. Rauf Ahmad, 2017. "Location-invariant Multi-sample U-tests for Covariance Matrices with Large Dimension," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 500-523, June.
    8. 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).
    9. M. Rauf Ahmad, 2019. "A unified approach to testing mean vectors with large dimensions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(4), pages 593-618, December.
    Full references (including those not matched with items on IDEAS)

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