Shape2SSCM transforms the theoretical shape matrix of an elliptical distribution into the spatial sign covariance matrix.
(required) p x p matrix representing the theoretical shape matrix.
The calculation consists of three steps. First one calculates eigenvectors and eigenvalues of the shape matrix by the function
eigen. Then one determines the related eigenvalues of the SSCM using the function
evShape2evSSCM and finally one expands the resulting eigendecomposition consisting of the eigenvectors of the Shape matrix and the eigenvalues of the SSCM. Note that this procedure only works for elliptical distributions.
p x p symmetric numerical matrix, representing the spatial sign covariance matrix, which corresponds to the given shape matrix.
Dürre, A., Vogel, D., Fried, R. (2015): Spatial sign correlation, Journal of Multivariate Analyis, vol. 135, 89–105. arvix 1403.7635
Dürre, A., Tyler, D. E., Vogel, D. (2016): On the eigenvalues of the spatial sign covariance matrix in more than two dimensions, to appear in: Statistics and Probability Letters. arvix 1512.02863
Calculating the theoretical shape from the theoretical SSCM
Calculating the eigenvalues of the SSCM
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