Oja Signed Ranks – Affine Equivariant Multivariate Signed Ranks

Description

The function computes the Oja signed rank of a point x w.r.t. a data set X or, if no point x is given, the Oja signed ranks of all points in X.

Usage

ojaSignedRank(X, x = NULL, p = NULL, silent = FALSE, 
              na.action = na.fail)

Arguments

Details

The function computes the Oja signed rank of the point x w.r.t. the data set X or, if no x is specified, the Oja signed ranks of all data points in X w.r.t. X. For a definition of Oja signed rank see Hettmansperger et al. (1997) formula (9).

The matrix X needs to have at least as many rows as columns in order to give sensible results. The vector x has to be of length ncol(X). If x is specified, a vector of length ncol(X) is returned. Otherwise the return value is a matrix of the same dimensions as X where the i-th row contains the Oja rank of the i-th row of X.

The function will also work for matrices X with only one column and also vectors. Then (univariate) signed ranks are returned.

For n = nrow(X) data points in R^k, where k = ncol(X), the computation of the Oja signed rank necessitates the evaluation of N = 2^k*choose(n,k) hyperplanes in R^k. Thus for large data sets the function offers a subsampling option in order to deliver (approximate) results within reasonable time. The subsampling fraction is controlled by the parameter p: If p < 1 is passed to the function, the computation is based on a random sample of only p N of all possible N hyperplanes. If p is not specified (which defaults to p = NULL), it is automatically determined based on n and k to yield a sensible trade-off between accuracy and computing time. If 2^k*choose(n,k)*k^3 < 6e+06, the sample fraction p is set to 1 (no subsampling). If all Oja signed ranks of X are requested, a hyperplane sample is drawn once and all Oja signed ranks are then computed based on this sample.

Finally, subsampling is feasible. Even for very small p useable results can be expected, see e.g. the examples for the function ojaRCM.

Value

Either a numeric vector, the Oja signed rank of x, or a matrix of the same dimensions as X containing the Oja signed ranks of X as rows.

Author(s)

Jyrki M<c3><83><c2><b6>tt<c3><83><c2><b6>nen

References

Hettmansperger, T. P., M<c3><83><c2><b6>tt<c3><83><c2><b6>nen, J. and Oja, H. (1997), Affine invariant multivariate one-sample signed-rank tests, J. Amer. Statist. Assoc., 92, 1591–1600.

Oja, H. (1999), Affine invariant multivariate sign and rank tests and corresponding estimates: A review, Scand. J. Statist., 26, 319–343.

See Also

ojaSign, ojaRank, ojaRCM, hyperplane

Examples

set.seed(123)
X <- rmvnorm(n = 30,mean = c(0,0)) # from package 'mvtnorm'
ojaSignedRank(X)
ojaSignedRank(X, x = c(0,0)) # zero

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(OjaNP)
Loading required package: ICS
Loading required package: mvtnorm
Loading required package: ICSNP
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/OjaNP/ojaSignedRank.Rd_%03d_medium.png", width=480, height=480)
> ### Name: ojaSignedRank
> ### Title: Oja Signed Ranks - Affine Equivariant Multivariate Signed Ranks
> ### Aliases: ojaSignedRank
> ### Keywords: multivariate nonparametric
> 
> ### ** Examples
> 
> set.seed(123)
> X <- rmvnorm(n = 30,mean = c(0,0)) # from package 'mvtnorm'
> ojaSignedRank(X)
              [,1]        [,2]
 [1,] -0.495140906 -0.24248888
 [2,]  1.028715285  0.08127564
 [3,]  0.290188478  0.83185037
 [4,]  0.261757295 -0.62036253
 [5,] -0.617016938 -0.42697620
 [6,]  0.965337851  0.31815463
 [7,]  0.324103284  0.08202580
 [8,] -0.255796333  0.74927547
 [9,]  0.104023629 -0.81706011
[10,]  0.574884606 -0.34072745
[11,] -0.911789729 -0.18248099
[12,] -0.845432808 -0.55862003
[13,] -0.518000955 -0.80814898
[14,]  0.781225701  0.12052760
[15,] -0.665767368  0.51360039
[16,]  0.337555068 -0.28010413
[17,]  0.709049387  0.69609915
[18,]  0.682462121  0.59246065
[19,]  0.508356007 -0.09618360
[20,] -0.232840180 -0.37640266
[21,] -0.648673437 -0.20551265
[22,] -0.518867112  0.65524719
[23,]  0.779176672 -0.41907208
[24,] -0.346124229 -0.47628708
[25,]  0.726637949 -0.09176243
[26,]  0.182886537 -0.06540457
[27,]  0.150310507  0.74652224
[28,]  0.005639374  0.75941964
[29,] -0.954536980  0.20182180
[30,]  0.055605876  0.20560378
> ojaSignedRank(X, x = c(0,0)) # zero
[1]  0.000000e+00 -2.990903e-21
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>