On the variability of the sample covariance matrix under complex elliptical distributions
Statistics Theory
2021-11-10 v2 Statistics Theory
Abstract
We derive the form of the variance-covariance matrix for any affine equivariant matrix-valued statistics when sampling from complex elliptical distributions. We then use this result to derive the variance-covariance matrix of the sample covariance matrix (SCM) as well as its theoretical mean squared error (MSE) when finite fourth-order moments exist. Finally, illustrative examples of the formulas are presented.
Cite
@article{arxiv.2108.08047,
title = {On the variability of the sample covariance matrix under complex elliptical distributions},
author = {Elias Raninen and Esa Ollila and David E. Tyler},
journal= {arXiv preprint arXiv:2108.08047},
year = {2021}
}