CovSest {rrcov} | R Documentation |
Computes S-Estimates of multivariate location and scatter based on Tukey's biweight function using a fast algorithm similar to the one proposed by Salibian-Barrera and Yohai (2006) for the case of regression. Alternativley, the Ruppert's SURREAL algorithm, bisquare or Rocke type estimation can be used.
CovSest(x, bdp = 0.5, arp = 0.1, eps = 1e-5, maxiter = 120, nsamp = 500, seed = NULL, trace = FALSE, tolSolve = 1e-13, method = c("sfast", "surreal", "bisquare", "rocke"), control, t0, S0, initcontrol)
x |
a matrix or data frame. |
bdp |
required breakdown point. Allowed values are between
(n - p)/(2 * n) and 1 and the default is 0.5 |
arp |
a numeric value specifying the asympthotic
rejection point (for the Rocke type S estimates),
i.e. the fraction of points receiving zero
weight (see Rocke (1996)). Default is 0.1
|
eps |
a numeric value specifying the
relative precision of the solution of the S-estimate (bisquare and Rocke type).
Defaults to 1e-5 .
|
maxiter |
maximum number of iterations allowed in the computation of the S-estimate (bisquare and Rocke type). Defaults to 120. |
nsamp |
the number of random subsets considered. Default is nsamp = 500 |
seed |
starting value for random generator. Default is seed = NULL . |
trace |
whether to print intermediate results. Default is trace = FALSE . |
tolSolve |
numeric tolerance to be used for inversion
(solve ) of the covariance matrix in
mahalanobis . |
method |
Which algorithm to use: 'sfast'=FAST-S, 'surreal'=SURREAL, 'bisquare' or 'rocke' |
control |
a control object (S4) of class CovControlSest-class
containing estimation options - same as these provided in the fucntion
specification. If the control object is supplied, the parameters from it
will be used. If parameters are passed also in the invocation statement, they will
override the corresponding elements of the control object. |
t0 |
optional initial HBDP estimate for the center |
S0 |
optional initial HBDP estimate for the covariance matrix |
initcontrol |
optional control object to be used for computing the initial HBDP estimates |
Computes biweight multivariate S-estimator of location and scatter. The computation will be performed by one of the following algorithms:
method
is set to 'surreal'method
set to 'bisquare'method
set to 'rocke'
An S4 object of class CovSest-class
which is a subclass of the
virtual class CovRobust-class
.
Valentin Todorov valentin.todorov@chello.at and Matias Salibian-Barrera matias@stat.ubc.ca. See also the code from Kristel Joossens, K.U. Leuven, Belgium and Ella Roelant, Ghent University, Belgium.
H.P. Lopuhaä (1989) On the Relation between S-estimators and M-estimators of Multivariate Location and Covariance. Annals of Statistics 17 1662–1683.
D. Ruppert (1992) Computing S Estimators for Regression and Multivariate Location/Dispersion. Journal of Computational and Graphical Statistics 1 253–270.
M. Salibian-Barrera and V. Yohai (2006) A fast algorithm for S-regression estimates, Journal of Computational and Graphical Statistics, 15, 414–427.
R. A. Maronna, D. Martin and V. Yohai (2006). Robust Statistics: Theory and Methods. Wiley, New York.
library(rrcov) data(hbk) hbk.x <- data.matrix(hbk[, 1:3]) CovSest(hbk.x) ## the following four statements are equivalent c0 <- CovSest(hbk.x) c1 <- CovSest(hbk.x, bdp = 0.25) c2 <- CovSest(hbk.x, control = CovControlSest(bdp = 0.25)) c3 <- CovSest(hbk.x, control = new("CovControlSest", bdp = 0.25)) ## direct specification overrides control one: c4 <- CovSest(hbk.x, bdp = 0.40, control = CovControlSest(bdp = 0.25)) c1 summary(c1) plot(c1) ## Use the SURREAL algorithm of Ruppert cr <- CovSest(hbk.x, method="surreal") cr ## Use Bisquare estimation cr <- CovSest(hbk.x, method="bisquare") cr ## Use Rocke type estimation cr <- CovSest(hbk.x, method="rocke") cr