We gather several results on the eigenvalues of the spatial sign covariance matrix of an elliptical distribution. It is shown that the eigenvalues are a one-to-one function of the eigenvalues of the shape matrix and that they are closer together than the latter. We further provide a one-dimensional integral representation of the eigenvalues, which facilitates their numerical computation.
- Elliptical distribution
- Spatial Kendall’s tau matrix
- spatial sign covariance matrix
Dürre, A., Tyler, D. E., & Vogel, D. (2016). On the eigenvalues of the spatial sign covariance matrix in more than two dimensions. Statistics and Probability Letters, 111, 80-85. https://doi.org/10.1016/j.spl.2016.01.009