Description Usage Arguments Details Value References See Also Examples

`SSCM2Shape`

transforms the spatial sign covariance matrix of an elliptical distribution into its standardized shape matrix.

1 | ```
SSCM2Shape(V,itermax=100,tol=10^(-10))
``` |

`V` |
(required) p x p matrix representing the theoretical SSCM. |

`tol` |
(optional) numeric, defines the stopping rule of the approximation procedure, see the help of |

`itermax` |
(optional) numeric, defines the maximal number of iterations, see the help of |

The calculation consists of three steps. First one calculates eigenvectors and eigenvalues of the SSCM matrix by the function `eigen`

. Then one determines the eigenvalues of the related Shape matrix using the function `evSSCM2evShape`

. Finally one expands the eigendecomposition consisting of the eigenvectors of the SSCM and the eigenvalues of the shape matrix. The resulting shape matrix is standardized to have a trace of 1. Note that this procedure only works for elliptical distributions.

p x p symmetric numerical matrix, representing the shape matrix with trace 1, which corresponds to the spatial sign covariance 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 `SSCM2Shape`

Calculating the eigenvalues of the SSCM `evShape2evSSCM`

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
# defining a shape matrix with trace 1
V <- matrix(c(1,0.8,-0.2,0.8,1,0,-0.2,0,1),ncol=3)/3
V
# calculating the related SSCM
SSCM <- Shape2SSCM(V)
# recalculate the shape based on the SSCM
V2 <- SSCM2Shape(SSCM)
V2
# error is negligible
sum(abs(V-V2))
``` |

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