| Spatial sign and rank covariance matrices {SpatialNP} | R Documentation |
Spatial sign and rank covariance matrices
Description
Functions to compute spatial sign, spatial symmetrized sign, spatial rank and spatial signed rank covariance matrices
Usage
SCov(X, location = NULL, na.action = na.fail)
SSCov(X, na.action = na.fail)
RCov(X, na.action = na.fail)
SRCov(X, location = NULL, na.action = na.fail)
Arguments
X |
matrix or a data frame |
location |
numeric vector (may be missing) |
na.action |
a function which indicates what should happen when the data contain 'NA's. Default is to fail. |
Details
These functions compute the matrices of the form
ave \{S(x_i) S^T(x_i)\}
where S(x_i) are the appropriate scores of the data:
spatial signs, spatial symmetrized signs, spatial ranks or spatial
signed ranks. These are the so called outer standardization matrices
of location etc. tests based on spatial signs and ranks. They are
not affine equivariant.
SCov and SRCov require a location vector with respect
to which they are computed. If none is provided, SCov uses
spatial median and SRCov uses Hodges-Lehmann estimator.
Author(s)
Seija Sirkia, seija.sirkia@iki.fi
References
Visuri, S., Koivunen, V. and Oja, H. (2000). Sign and rank covariance matrices. J. Statistical Planning and Inference, 91, 557-575.
See Also
spatial signs and ranks, corresponding shape matrices (inner standardization matrices)
Examples
A<-matrix(c(1,2,-3,4,3,-2,-1,0,4),ncol=3)
X<-matrix(rt(150,1),ncol=3)%*%t(A)
SCov(X)
SSCov(X)
RCov(X)
SRCov(X)
to.shape(A%*%t(A),trace=1)