CovSest {rrcov}R Documentation

S Estimates of Multivariate Location and Scatter

Description

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 can be used.

Usage

    CovSest(x, nsamp = 500, bdp = 0.5, seed = NULL, trace = FALSE, tolSolve = 1e-13, 
        algo = c("sfast", "surreal"), control)

Arguments

x a matrix or data frame.
nsamp the number of random subsets considered. Default is nsamp = 500
bdp required breakdown point. Allowed values are between (n - p)/(2 * n) and 1 and the default is 0.5
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.
algo Which algorithm to use: 'sfast'=FAST-S or 'surreal'=SURREAL
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.

Details

Computes biweight multivariate S-estimator of location and scatter. The algorithm used is similar to the one proposed by Salibian-Barrera and Yohai (2006) for the case of regression. Alternativley, if the parameter algo is set to surreal the Ruppert's SURREAL algorithm will be used.

Value

An S4 object of class CovSest-class which is a subclass of the virtual class CovRobust-class.

Author(s)

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.

References

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.

Examples


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, algo="surreal")
cr

[Package rrcov version 0.4-05 Index]