rsmed {rsdepth}

Bivariate RS median

Description

Computes the Ray Shooting median of a bivariate data set.

Usage

rsmed(pt, eps=c(0),...)

Arguments

pt

The data as a matrix, data frame or list. If it is a matrix or data frame, then each row is viewed as one multivariate observation. If it is a list, all components must be numerical vectors of equal length (coordinates of observations). Only 2-dimensional data is acceptable in this version.

eps

eps is an optional parameter used for approximating a median in case of large data sets. It takes valye of a real between 0 and 1 and is by default set to 0 which means no approximation is used if eps is not given.

...

Reserved for future use.

Details

Finds out the an arbitrary point among the Ray Shooting median set of given point set. Current uses the brute-force algorithm on all O(n^4) possible points in the arrangment of all possible lines in complete graph on pt. For each point O(n log n) is used to find out depth so overall complexity of this algorithm is O(n^5 log n). When approximation parameter is provided then algorithm tries to approximate by finding median of a uniform sample subset of pt of size 1/eps^2*log(1/eps). If this constant is more than the size of original set then eps value is ignored and exact median is calculate on original point set.

Value

A point in two dimension is returned as a single row two column vector

Author(s)

Nabil Mustafa, Saurabh Ray, and Mudassir Shabbir.

References

N. Mustafa, S. Ray, and M. Shabbir, Statistical Data Depth of Pointsets in the Plane,in prep..

See Also

rsdepth for depth function

Examples

##  RS median of a two-dimensional data set
set.seed(617)
zz <- matrix(rnorm(120), nc = 2)
rsmed(zz,eps=0.2)