MMest_twosample {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

MMest_twosample(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 Sest_twosample, which uses a fast-S-type algorithm. Its tuning parameters can be changed via the control argument. The M-estimate part is computed through iteratively reweighted least squares (RWLS).

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)
w implicit weights corresponding to the MM-estimates (i.e. final weights in the RWLS procedure)
outFlag outlier flags: 1 if the robust distance of the observation exceeds the .975 quantile of (the square root of) the chi-square distribution with degrees of freedom equal to the dimension of Y; 0 otherwise

Author(s)

Ella Roelant and Gert Willems

References

See Also

Sest_twosample, FRBhotellingMM, MMboot_twosample, 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 <- MMest_twosample(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 1.6 Index]