twosampleS {FRB}R Documentation

Two Sample S-Estimates of Location and Covariance

Description

Computes two sample S-estimates of location and common covariance

Usage

twosampleS(X, groups, bdp = 0.5, control=Scontrol(...), ...)

Arguments

X matrix or data frame
groups vector of 1's and 2's, indicating group numbers
bdp required breakdown point of the two sample S-estimate. Should have 0 < bdp <= 0.5, the default is 0.5
control a list with control parameters for tuning the computing algorithm, see Scontrol().
... allows for specifying control parameters directly instead of via control

Details

This function is called by FRBhotellingS. The algorithm is a multivariate version of the fast-S algorithm introduced by Salibian-Barrera and Yohai (2006). See Scontrol for the adjustable tuning parameters of this algorithm.

The function both returns the covariance estimate Sigma and shape estimate Gamma (which has determinant equal to 1). The scale is determined by det(Sigma)^{1/2/p}, with p the number of variables.

Value

A list containing:

Mu1 S-estimate of first center
Mu2 S-estimate of second center
Sigma S-estimate of commmon covariance
Gamma S-estimate of common shape
scale S-estimate of scale (univariate)
b,c tuning parameters used in Tukey biweight loss function, as determined by bdp

Author(s)

Ella Roelant and Gert Willems

References

See Also

twosampleMM, FRBhotellingS, Sboottwosample, Scontrol

Examples

Y1 <- matrix(rnorm(50*5), ncol=5)
Y2 <- matrix(rnorm(50*5), ncol=5)
Ybig <- rbind(Y1,Y2)
grp <- c(rep(1,50),rep(2,50))
Sests <- twosampleS(Ybig, grp, bdp=0.25)
  
# S-estimate of first center:
Sests$Mu1
# S-estimate of second center:
Sests$Mu1
# S-estimate of common covariance:
Sests$Sigma


[Package FRB version 1.4 Index]