yamm.obj: Objective Function for Yamm

Description

The objective function when computing yamm, which is the integral of the squared or absolute value of the univariate median of the projection of the shifted data set over a unit hypersphere. It is implemented internally using C code Cyammobj and hence is much faster than coding with R only.

Usage

yamm.obj(x, mu, nprojs = 2000, doabs = 0)

Arguments

The data as a matrix or data frame, with each row being viewed as one multivariate observation.

A shift vector with length \(n\), where \(n\) should equal to the number of columns (variables) of the data matrix. Each row of the data matrix x is shifted by mu to obtain the shifted data matrix.

nprojs

The number of projections for the shifted data matrix while using the Monte Carlo method to approximate the integration. The default value is 2000.

doabs

If 0 (default), function yamm.obj integrates square of the univariate median of the projection to the shifted data set over a unit hypersphere; if 1, yamm.obj integrates absolute value of the univariate median instead.

Value

A univariate integral of the squared or absolute value of the median of the projection of the shifted data set over a unit hypersphere is returned from the .C calling function

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, 10.1371/journal.pone.0229845

Examples

Run this code

# NOT RUN {
data(beetle)
#
# Set seed for reproduction.
set.seed(5)
#
# Objective function for yamm with a chosen shift vector.
#
yamm.obj(beetle, mu=rep(10,6), nprojs=5000, doabs=1)
# [1] 88.38346
# }