Abstract
Test-statistics for testing covariance structures are examined for non-normal p-dimensional populations with the finite fourth-order mixed moments. Special attention has been paid to the sphericity and uncorrelatedness hypotheses. For the sphericity test, test-statistics based on trace functions are examined. A \(\chi ^2\)-statistic is constructed for the uncorrelatedness test. In a special case when all the fourth-order moments are equal, the results are simplified. Taylor expansions of the test-statistics have been derived, asymptotic normal and chi-square distributions have been established and their behaviour examined in the situation when both, sample size n and the number of variables p are growing when \(\frac{p}{n}<1\). A simulation experiment was carried out to investigate empirically speed of convergence to the asymptotic distributions depending on the sample size, the number of variables and the parameters of the population distribution.
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The authors are thankful to the Estonian Research Council for the financial support from the target financed project IUT34-5 and from the grant PRG1197.
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Kollo, T., Valge, M. (2021). On Testing Structures of the Covariance Matrix: A Non-normal Approach. In: Arnold, B.C., Balakrishnan, N., Coelho, C.A. (eds) Methodology and Applications of Statistics. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-83670-2_12
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