PmedTrapz: Projection Median Approximated by Trapezoidal Rule

In Yamm: Multivariate Methods Based on Projections and Related Concepts

Projection Median Approximated by Trapezoidal Rule

Description

This function approximates the projection median using trapezoidal rule, which is only valid for the two- and three-dimensional cases. PmedTrapz is implemented internally using C code CPmedTrapz2D and CPmedTrapz3D and hence is much faster than coding with R only.

Usage

PmedTrapz(x, no.subinterval)

Arguments

x	The data as a matrix or data frame, with each row being viewed as one multivariate observation.
no.subinterval	A vector of subintervals chosen for implementing the trapezoidal rule. It is a number in the two-dimensional case, and has a length of two for the three-dimensional data, since the trapezoidal rule is only required once in 2D and needs to be applied twice for the double integral in 3D. Small values (e.g. less than 10) for each entry of no.subinterval should not be used, to safeguard the accuracy.

Details

The projection median was introduced by Durocher and Kirkpatrick (2009) and generalised by Basu, Bhattacharya and Talukdar (2012). PmedTrapz produces the projection median directly from the definition using the trapezoidal rule, but current function is only valid in the two-dimensional and three-dimensional case. For more general dimensionalities, you can refer to function PmedMCInt and yamm.

Value

A vector of the projection median in the two or three dimensions.

References

Chen, F. and Nason, Guy P. (2020) A new method for computing the projection medi an, its influence curve and techniques for the production of projected quantile plots. PLOS One, doi: 10.1371/journal.pone.0229845

Durocher, S. and Kirkpatrick, D. (2009), The projection median of a set of points, Computational Geometry,42, 364-375.

Basu, R., Bhattacharya, B.B., and Talukdar, T. (2012) The projection median of a set of points in Rd CCCG., 47, 329-346. doi: 10.1007/s00454-011-9380-6

See Also

PmedMCInt

Examples

# Load a 2-dimensional dataset
data(clusters2d)
#
# Projection median approximated by the trapezoidal rule.
PmedTrapz(clusters2d,no.subinterval=180)
# [1]  4.1556553 -0.3566614
#
# Load a 3-dimensional dataset
data(clusters3d)
#
PmedTrapz(clusters3d,c(180,360))
# [1] -0.906680  1.584866  2.695584

Yamm documentation built on May 20, 2022, 5:06 p.m.