twosampleMM {FRB} | R Documentation |
Computes two-sample MM-estimates of multivariate location and common covariance, using initial two-sample S-estimates.
twosampleMM(X, groups, control=MMcontrol(...), ...)
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 |
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).
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 ) |
Ella Roelant and Gert Willems
twosampleS
, FRBhotellingMM
, MMboottwosample
, MMcontrol
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