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.
翻译:在从复杂的椭圆分布中取样时,我们得出任何等同矩阵估价统计数据的差异变量矩阵形式。然后,我们利用这一结果得出样本变量矩阵的差异变量矩阵,以及在存在限定的第四阶时的理论平均正方差错误(MSE)。最后,提供了公式示例。