Far East Journal of Theoretical Statistics
Volume 14, Issue 1, Pages 33 - 46
(September 2004)
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INDEPENDENCE DISTRIBUTION-PRESERVING JOINT COVARIANCE STRUCTURES FOR SAMPLE COVARIANCE MATRICES
Dean M. Young (U. S. A.), David A. Paul (U. S. A.) and Danny W. Turner (U. S. A.)
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Abstract: We characterize the general nonnegative-definite joint observation covariance structure under which sample covariance matrices composed of data from two populations are distributed as multiples of independent noncentral or central Wishart random matrices. We formulate and utilize a new representation of the general common nonnegative-definite solution of a certain system of matrix equations as the key element in the characterization derivation. |
Keywords and phrases: common nonnegative-definite solutions to matrix equations, independence and identical distribution assumptions, multivariate quadratic forms, Wishart random matrices. |
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