Spatial signs, symmetrized signs, ranks and signed ranks {SpatialNP} | R Documentation |
Spatial signs, symmetrized signs, ranks and signed ranks
Description
Functions to compute spatial signs, symmetrized signs, ranks and signed ranks.
Usage
spatial.signs(X, center = TRUE, shape = TRUE,
na.action = na.fail,...)
spatial.symmsign(X, shape = TRUE, na.action = na.fail, ...)
spatial.rank(X, shape = TRUE, na.action = na.fail, ...)
spatial.signrank(X, center = TRUE, shape = TRUE,
na.action = na.fail,...)
Arguments
X |
a matrix or a data frame |
center |
a vector or a logical, see details |
shape |
a matrix or a logical, see details |
... |
arguments that can be passed on to function used for the estimation of shape. |
na.action |
a function which indicates what should happen when the data contain 'NA's. Default is to fail. |
Details
The spatial signs of an observed vector is simply the
vector, possibly affinely transformed first, multiplied by its
Euclidian length. See spatial.sign
for a precise
definition. Symmetrized spatial signs are the spatial signs of the pairwise
differences of the data
||x_i-x_j||^{-1}(x_i-x_j)
(there are n
over 2 of these). Spatial
rank of an observation is the average of the signs of the differences
of that observation and the others:
R(x_i)=ave_j\{||x_i-x_j||^{-1}(x_i-x_j)\}
Spatial signed rank of an observation is defined as
Q(x_i)=(R(x_i)+ave_j\{||x_i+x_j||^{-1}(x_i+x_j)\})/2
If a numerical value is given for shape
and/or center
these are used to transform the data before the computation of signs
or ranks. A logical TRUE
indicates that the shape or center should be
estimated. In this case an affine transformation that makes the
resulting signs or ranks have a covariance matrix equal or
proportional to the identity matrix and centerd on the origin is
found. A logical FALSE
indicates that the null value, that is, the
identity matrix or the origin, should be used. Note that only signed
ranks depend on a center.
The value of shape and/or location used are returned as attributes.
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.sign
for the signs, spatial sign and rank covariance matrices and spatial.shape
for the standardizing transformations
Examples
A<-matrix(c(1,2,-3,4),ncol=2)
X<-matrix(rnorm(100),ncol=2)%*%t(A)
def.par<-par(no.readonly=TRUE) # for resetting
layout(matrix(1:4,ncol=2,nrow=2,byrow=TRUE))
plot(X,col=c(2,rep(1,19)))
plot(spatial.symmsign(X),col=c(2,rep(1,19)),xlim=c(-1,1),ylim=c(-1,1))
theta<-seq(0,2*pi,length=1000)
lines(sin(theta),cos(theta))
plot(spatial.rank(X),col=c(2,rep(1,19)),xlim=c(-1,1),ylim=c(-1,1))
lines(sin(theta),cos(theta))
plot(spatial.signrank(X),col=c(2,rep(1,19)),xlim=c(-1,1),ylim=c(-1,1))
lines(sin(theta),cos(theta))
par(def.par)