outlyingness {andrews}

outlyingness

Description

Computes the Stahel-Donoho outlyingness. If type is any of the available types by andrews() then the projection vectors are generated along the andrews curves. Otherwise step random directions will be used. Note that the projection vectors are always normalized to length one.

Usage

outlyingness(x, type = 1, step = 100, xlim = NULL, normalize = 1)

Arguments

x

data frame

type

type of curve, see andrews()

step

step smoothness of curves

xlim

the x limits (x1, x2)

normalize

type of normalization, see normalize()

Value

the Stahel-Donoho outlyingness

References

• Stahel, W. (1981), Robuste Schätzungen: infinitesimale Optimalität und Schätzungen von Kovarianzmatrizen, PhD thesis, ETH Z¨urich.

• Donoho, D. (1982), Breakdown properties of multivariate location estimators, Ph.D. Qualifying paper, Dept. Statistics, Harvard University, Boston.

Examples

# use projection vectors from the Andrews curve
sdo <- outlyingness(iris)
col <- gray(1-sdo/max(sdo))
andrews(iris, clr=col, ymax=NA)
# use 1000 random projection vectors
sdo <- outlyingness(iris, type=0, step=1000)
col <- gray(1-sdo/max(sdo))
andrews(iris, clr=col, ymax=NA)
# use 1000 random projection vectors with adjusted outlyingness
library("robustbase")
x   <- numarray(iris)
x   <- scale(x, center=apply(x, 2, min), scale=apply(x, 2, max)-apply(x, 2, min))
sdo <- adjOutlyingness(x, ndir=1000, only.outlyingness=TRUE)
col <- gray(1-sdo/max(sdo))
andrews(as.data.frame(x), clr=col, ymax=NA)