Sest_twosample {FRB} | R Documentation |
Computes two sample S-estimates of location and common covariance
Sest_twosample(X, groups, bdp = 0.5, control=Scontrol(...), ...)
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 |
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.
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 |
w |
implicit weights corresponding to the S-estimates (i.e. final weights in the RWLS procedure at the end of the fast-S algorithm) |
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 X ; 0 otherwise |
Ella Roelant and Gert Willems
MMest_twosample
, FRBhotellingS
, Sboot_twosample
, Scontrol
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 <- Sest_twosample(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