Nonnegative-definite independence distribution-preserving covariance structures for the sample covariance matrix : theory and methods

We explicitly characterize the general mean matrix and the general nonnegative-definite covariance structure of a matrix-normal random matrix such that the multivariate sample covariance matrix is distributed as a central Wishart random matrix. We also characterize the general mean matrix and the general nonnegative-definite covariance structure of a matrix-normal random matrix such that the sample covariance matrix is distributed as a central Wishart random matrix and is independent of the sample mean vector.