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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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