Abstract
This paper verifies if the classical test to sphericity hypotheses with homogeneous variances equal to one and null covariances is applicable for cases in the presence of outliers based on four different tests performed to verify its robustness. The classical likelihood ratio test (LTR) is applied and we also propose some of its modifications in wich the sample covariance matrix is switched by one of its robust estimators, and since there is an assumption violation due to the presence of outliers, a Monte Carlo version of both asymptotic versions is considered. The normal and contaminated normal distributions are also considered. In conclusion, two of the tests are robust in the presence of outliers in a multivariate normal distribution: the Monte Carlo version of the original test (LRTMC) and the Monte Carlo version of the modified test where the sample covariance matrix is switched by the comedian estimator (LRTMCR), and the most powerful test is LRTMC.
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The data were obtained through simulations and they are available in the tables presented in the article.
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Acknowledgements
This work was carried out with the support of the Coordination of Improvement of Higher Education Personnel - Brazil (CAPES) - Financing Code 001. The authors would like to thank Luiz Matheus Barbosa Santos for his valuable contribution with the English presentation, and to the scientific computing laboratory of the Department of Physics (DFI) for access to the server to assist in the simulations of the data.
Funding
This work was carried out with the support of the Coordination of Improvement of Higher Education Personnel - Brazil (CAPES) - Financing Code 001.
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Campos, L.L., Ferreira, D.F. Robust modified classical spherical tests in the presence of outliers. Stat Papers 63, 1561–1576 (2022). https://doi.org/10.1007/s00362-022-01289-w
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DOI: https://doi.org/10.1007/s00362-022-01289-w