ojaSignedRank: Oja Signed Ranks - Affine Equivariant Multivariate Signed...

In fischuu/OjaNP: Multivariate Methods Based on the Oja Median and Related Concepts

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

X	numeric data.frame or matrix containing the data points as rows.
x	NULL or a numeric vector, the point for which the Oja signed rank should be computed.
p	NULL or a number between 0 and 1 which specifies the fraction of hyperplanes to be used for subsampling. If p = 1, no subsampling is done. If p = NULL, the value of p is determined based on the size of the data set. See details.
silent	logical, if subsampling is done or the expected computation time is too long, a warning message will be printed unless silent is TRUE. The default is FALSE.
na.action	a function which indicates what should happen when the data contain 'NA's. Default is to fail.

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 N k^3 < 6 \cdot 10^6, 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 Möttönen

References

Fischer D, Mosler K, Möttönen J, Nordhausen K, Pokotylo O and Vogel D (2020). “Computing the Oja Median in R: The Package OjaNP.” Journal of Statistical Software, 92(8), pp. 1-36. doi: 10.18637/jss.v092.i08 (URL: http://doi.org/10.18637/jss.v092.i08).

Hettmansperger, T. P.,\ Möttönen, 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

fischuu/OjaNP documentation built on April 19, 2023, 9:50 a.m.