rrcov (version 0.4-08)

CovSest: 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, bisquare or Rocke type estimation can be used.

Usage

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)

Arguments

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 para

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

Value

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

encoding

latin1

concept

High breakdown point

Details

Computes biweight multivariate S-estimator of location and scatter. The computation will be performed by one of the following algorithms: [object Object],[object Object],[object Object],[object Object],.

References

H.P. Lopuha� (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.

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, method="surreal")
cr

## Use Bisquare estimation
cr <- CovSest(hbk.x, method="bisquare")
cr

## Use Rocke type estimation
cr <- CovSest(hbk.x, method="rocke")
cr