slc {riv}R Documentation

S-estimator of multivariate location and covariance

Description

Finds the robust S-estimator of multivariate location and covariance with a high breakdown point based on Tukey's biweight function.

Usage

slc(x, nsamp = 500, bdp = 0.5)

Arguments

x a matrix or data frame of data values, say of dimension n x p. The rows represent observations and the columns represent variables.
nsamp the number of random p-subsets considered to compute the S-estimator (default = 500).
bdp breakdown point value of the S-estimator, must be 0.15,0.25 or 0.5 (default).

Value

A list with components

location vector of the estimated multivariate location.
covariance matrix of the estimated covariance.
distances vector of robust Mahalanobis distances versus location and covariance.
scale distance of the scale estimates.
c constant of the Tukey's biweight function.

Author(s)

Kaufmann B. beat.kaufmann@epfl.ch

Cohen-Freue G.V. gcohen@stat.ubc.ca

Zamar R.H. ruben@stat.ubc.ca

References

LOPUHAÄ,H.P. (1989) On the Relation between S-estimators and M-estimators of Multivariate Location and Covariance. Ann. Statist. 17 1662-1683.

RUPPERT,D. (1992). Computing S Estimators for Regression and Multivariate Location/Dispersion. J. Comput. Graph. Statist. 1 253-270.

See Also

lqs

Examples

 
library(MASS)
## load the mortality data-set (62 Alaskan earthquake observations)
data(mortality)
slc.res <- slc(mortality,nsamp=100,bdp=0.25)   

## plot of the Mahalanobis Distances
plot(slc.res[[3]],xlab="Observation",ylab="Mahalanobis Distance",main="The Mahalanobis Distance of each observation")   

## simulation of a multivariate data-set
library(MASS)
x <- mvrnorm(100,c(0,0,0),matrix(c(1,0,0,0,1,0.5,0,0.5,1),ncol=3))

slc(x,nsamp=50,bdp=0.15)

[Package riv version 1.0-1 Index]