Shape2SSCM {sscor}

Calculation of the Spatial Sign Covariance Matrix

Description

Shape2SSCM transforms the theoretical shape matrix of an elliptical distribution into the spatial sign covariance matrix.

Usage

Shape2SSCM(V)

Arguments

V

(required) p x p matrix representing the theoretical shape matrix.

Details

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.

Value

p x p symmetric numerical matrix, representing the spatial sign covariance matrix, which corresponds to the given shape matrix.

References

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

See Also

Calculating the theoretical shape from the theoretical SSCM SSCM2Shape

Calculating the eigenvalues of the SSCM evShape2evSSCM

Examples

# 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))