# spatialsignsranks: Spatial signs, symmetrized signs, ranks and signed ranks In SpatialNP: Multivariate Nonparametric Methods Based on Spatial Signs and Ranks

## Description

Functions to compute spatial signs, symmetrized signs, ranks and signed ranks.

## Usage

 ```1 2 3 4 5 6``` ```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, [email protected]

## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```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) ```

SpatialNP documentation built on June 6, 2018, 1:06 a.m.