On the variability of the sample covariance matrix under complex elliptical distributions

08/18/2021

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by   Elias Raninen, et al.

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We derive the variance-covariance matrix of the sample covariance matrix (SCM) as well as its theoretical mean squared error (MSE) when sampling from complex elliptical distributions with finite fourth-order moments. We also derive the form of the variance-covariance matrix for any affine equivariant matrix-valued statistics. Finally, illustrative examples of the formulas are presented.