## Self similar compound symmetry covariance structure.(English)Zbl 1477.62129

Summary: Self similar compound symmetry (SSCS) covariance structure is introduced and studied. The $$k$$-SSCS covariance structure (defined in Sect. 3) for array-variate $$k$$th order data incorporates the exchangeable feature of $$k$$-dimensional arrays into the model. 3-SSCS covariance structure or double block compound symmetry covariance structure for array-variate 3rd order data is a generalization of 2-SSCS covariance structure or block compound symmetry covariance structure for the matrix-variate 2nd order data, which in turn is a generalization of compound symmetry covariance structure for traditional vector-variate (multivariate) 1st order data. This article generalizes this compound symmetry covariance structure for array-variate $$k$$th order data, and we name it as “$$k$$ self similar compound symmetry” ($$k$$SSCS) covariance structure. This is of critical importance to a variety of applied problems in agricultural, biomedical, medical, environmental, engineering and space missions among many other fields with $$k$$-dimensional array-variate data. The proposed method is illustrated with a medical dataset.

### MSC:

 62H10 Multivariate distribution of statistics 62H12 Estimation in multivariate analysis 62P10 Applications of statistics to biology and medical sciences; meta analysis
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### References:

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