Testing hypotheses about correlation matrices in general MANOVA designs

Paavo Sattler () and Markus Pauly ()
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Paavo Sattler: TU Dortmund University
Markus Pauly: TU Dortmund University

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2024, vol. 33, issue 2, No 6, 496-516

Abstract: 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.

Keywords: Bootstrap; Multivariate data; Nonparametric testing; Resampling; Correlation matrices; Quadratic forms; 62H15; 62G09; 62G10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11749-023-00906-6

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