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A significance test of the RV coefficient in high dimensions

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  • Rauf Ahmad, M.

Abstract

The RV coefficient is an important measure of linear dependence between two multivariate data vectors. Using unbiased and computationally efficient estimators of its components, a modification to the RV coefficient is proposed, and used to construct a test of significance for the true coefficient. The modified estimator improves the accuracy of the original and, along with the test, can be applied to data with arbitrarily large dimensions, possibly exceeding the sample size, and the underlying distribution need only have finite fourth moment. Exact and asymptotic properties are studied under fairly general conditions. The accuracy of the modified estimator and the test is shown through simulations under a variety of parameter settings. In comparisons against several existing methods, both the proposed estimator and the test exhibit similar performance to the distance correlation. Several real data applications are also provided.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:131:y:2019:i:c:p:116-130
    DOI: 10.1016/j.csda.2018.10.008
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    References listed on IDEAS

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    2. Xiang Zhan & Anna Plantinga & Ni Zhao & Michael C. Wu, 2017. "A fast small‐sample kernel independence test for microbiome community‐level association analysis," Biometrics, The International Biometric Society, vol. 73(4), pages 1453-1463, December.
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    8. 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.
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    1. Ahmad, Rauf, 2022. "Tests for proportionality of matrices with large dimension," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

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