twosampleMM {FRB}R Documentation

Two Sample MM-Estimates of Location and Covariance

Description

Computes two-sample MM-estimates of multivariate location and common covariance, using initial two-sample S-estimates.

Usage

twosampleMM(X, groups, control=MMcontrol(...), ...)

Arguments

X matrix or data frame
groups vector of 1's and 2's, indicating group numbers
control a list with control parameters for tuning the MM-estimate and its computing algorithm, see MMcontrol().
... allows for specifying control parameters directly instead of via control

Details

This function is called by FRBhotellingMM

The two-sample MM-estimates are defined by first computing a two-sample S-estimate of location for each sample and common covariance, then fixing its scale component and re-estimating the location vectors and shape by a more efficient M-estimate (see Tatsuoka and Tyler (2000)). Tukey's biweight is used for the loss functions. By default, the first loss function (in the two-sample S-estimate) is tuned in order to obtain 50% breakdown point. The default tuning of the second loss function (M-estimate) ensures 95% efficiency at the normal model. This tuning can be changed via argument control if desired.

The computation of the two-sample S-estimate is performed by a call to twosampleS, which uses a fast-S-type algorithm. Its tuning parameters can be changed via the control argument.

Apart from the MM-location estimates Mu1 and Mu2, the function returns both the common MM-covariance Sigma and common MM-shape estimate Gamma (which has determinant equal to 1). Additionally, the S-estimates are returned as well (their Gaussian efficiency is usually lower than the MM-estimates but they may have a lower bias).

Value

A list containing:

Mu1 MM-estimate of first center
Mu2 MM-estimate of second center
Sigma MM-estimate of covariance
Gamma MM-estimate of shape
SMu1 S-estimate of first center
SMu2 S-estimate of second center
SSigma S-estimate of covariance
SGamma S-estimate of shape
scale S-estimate of scale (univariate)
c0,b,c1 tuning parameters of the loss functions (depend on control parameters bdp and eff)

Author(s)

Ella Roelant and Gert Willems

References

See Also

twosampleS, FRBhotellingMM, MMboottwosample, MMcontrol

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))
MMests <- twosampleMM(Ybig, grp)

# MM-estimate of first center:
MMests$Mu1
# MM-estimate of second center:
MMests$Mu1
# MM-estimate of common covariance:
MMests$Sigma
#initial S-estimate of first center:
MMests$SMu1
#initial S-estimate of second center:
MMests$SMu2

[Package FRB version 1.4 Index]