Sest_loccov {FRB} | R Documentation |
Computes S-estimates of multivariate location and covariance using the fast-S algorithm
Sest_loccov(Y, bdp = 0.5, control=Scontrol(...), ...)
Y |
matrix or data frame |
bdp |
required breakdown point of the 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 FRBpcaS
and FRBhotellingS
.
Multivariate S-estimates were introduced by Davies (1987). The algorithm used here 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:
Mu |
S-estimate of location |
Gamma |
S-estimate of shape |
Sigma |
S-estimate of covariance |
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 Y ; 0 otherwise |
Gert Willems and Ella Roelant
FRBpcaS
, FRBhotellingS
, Sboot_loccov
, MMest_loccov
, Scontrol
Y <- matrix(rnorm(50*5), ncol=5) Sests <- Sest_loccov(Y, bdp = 0.25) # S-estimate of location: Sests$Mu # S-estimate of covariance: Sests$Sigma