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Approximate normality in testing an exchangeable covariance structure under large- and high-dimensional settings

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  • Klein, Daniel
  • Pielaszkiewicz, Jolanta
  • Filipiak, Katarzyna

Abstract

In this paper the Rao score and likelihood ratio tests for hypothesis related to exchangeable structure of multivariate data covariance matrix are studied. Under the assumption of large-dimensionality the normal approximation of the Rao score test statistics distribution is proven as well as the exact and approximate distributions of the likelihood ratio test are derived. Simulation studies show the advantage of the Rao score test over the likelihood ratio test in both studied contexts: type I error and power. Moreover, the Rao score test is available in the case of high-dimensionality, and it is shown that the normal approximation matches well its distribution in this case. Thus, this latter approximation could be recommended for practical use.

Suggested Citation

  • Klein, Daniel & Pielaszkiewicz, Jolanta & Filipiak, Katarzyna, 2022. "Approximate normality in testing an exchangeable covariance structure under large- and high-dimensional settings," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:jmvana:v:192:y:2022:i:c:s0047259x22000616
    DOI: 10.1016/j.jmva.2022.105049
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    References listed on IDEAS

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    5. Gérard Letac & Hélène Massam, 2004. "All Invariant Moments of the Wishart Distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(2), pages 295-318, June.
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