The asymptotic inadmissibility of the spatial sign covariance matrix for elliptically symmetric distributions
椭圆对称分布下空间符号协方差矩阵的渐近不可容许性
The asymptotic efficiency of the spatial sign covariance matrix relative to affine equivariant estimators of scatter is studied. In particular, the spatial sign covariance matrix is shown to be asymptotically inadmissible, i.e., the asymptotic covariance matrix of the consistency-corrected spatial sign covariance matrix is uniformly larger than that of its affine equivariant counterpart, namely Tyler’s scatter matrix. Although the spatial sign covariance matrix has often…