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Testing hypotheses about correlation matrices in general MANOVA designs

Author

Listed:
  • Paavo Sattler

    (TU Dortmund University)

  • Markus Pauly

    (TU Dortmund University
    UA Ruhr)

Abstract

Correlation matrices are an essential tool for investigating the dependency structures of random vectors or comparing them. We introduce an approach for testing a variety of null hypotheses that can be formulated based upon the correlation matrix. Examples cover MANOVA-type hypothesis of equal correlation matrices as well as testing for special correlation structures such as sphericity. Apart from existing fourth moments, our approach requires no other assumptions, allowing applications in various settings. To improve the small sample performance, a bootstrap technique is proposed and theoretically justified. Based on this, we also present a procedure to simultaneously test the hypotheses of equal correlation and equal covariance matrices. The performance of all new test statistics is compared with existing procedures through extensive simulations.

Suggested Citation

  • Paavo Sattler & Markus Pauly, 2024. "Testing hypotheses about correlation matrices in general MANOVA designs," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(2), pages 496-516, June.
    • Handle: RePEc:spr:testjl:v:33:y:2024:i:2:d:10.1007_s11749-023-00906-6
    DOI: 10.1007/s11749-023-00906-6
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    References listed on IDEAS

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    1. Nowak, Claus P. & Konietschke, Frank, 2021. "Simultaneous inference for Kendall’s tau," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    2. Gaißer, Sandra & Schmid, Friedrich, 2010. "On testing equality of pairwise rank correlations in a multivariate random vector," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2598-2615, November.
    3. Arjun Gupta & Jin Xu, 2006. "On Some Tests of the Covariance Matrix Under General Conditions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(1), pages 101-114, March.
    4. Tian, Lili & Wilding, Gregory E., 2008. "Confidence interval estimation of a common correlation coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4872-4877, June.
    5. Friedrich, Sarah & Brunner, Edgar & Pauly, Markus, 2017. "Permuting longitudinal data in spite of the dependencies," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 255-265.
    6. Umlauft, Maria & Placzek, Marius & Konietschke, Frank & Pauly, Markus, 2019. "Wild bootstrapping rank-based procedures: Multiple testing in nonparametric factorial repeated measures designs," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 176-192.
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