rrcov (version 1.3-8)

CovMMest: MM Estimates of Multivariate Location and Scatter

Description

Computes MM-Estimates of multivariate location and scatter starting from an initial S-estimate

Usage

CovMMest(x, bdp = 0.5, eff = 0.95, eff.shape=TRUE, maxiter = 50, 
        trace = FALSE, tolSolve = 1e-7, control)

Arguments

x

a matrix or data frame.

bdp

a numeric value specifying the required breakdown point. Allowed values are between 0.5 and 1 and the default is bdp=0.5.

eff

a numeric value specifying the required efficiency for the MM estimates. Default is eff=0.95.

eff.shape

logical; if TRUE, eff is with regard to shape-efficiency, otherwise location-efficiency. Default is eff.shape=FALSE.

maxiter

maximum number of iterations allowed in the computation of the S-estimate (bisquare and Rocke type). Default is maxiter=50.

trace

whether to print intermediate results. Default is trace = FALSE.

tolSolve

numeric tolerance to be used as a convergence tolerance for the MM-iteration

control

a control object (S4) of class CovControlMMest-class containing estimation options - same as these provided in the fucntion specification. If the control object is supplied, the para

Value

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

encoding

latin1

concept

High breakdown point

Details

Computes MM-estimates of multivariate location and scatter starting from an initial S-estimate.

References

Tatsuoka, K.S. and Tyler, D.E. (2000). The uniqueness of S and M-functionals under non-elliptical distributions. Annals of Statistics 28, 1219--1243 M. Salibian-Barrera, S. Van Aelstt and G. Willems (2006). Principal components analysis based on multivariate MM-estimators with fast and robust bootstrap. Journal of the American Statistical Association 101, 1198--1211. R. A. Maronna, D. Martin and V. Yohai (2006). Robust Statistics: Theory and Methods. Wiley, New York. Todorov V & Filzmoser P (2009), An Object Oriented Framework for Robust Multivariate Analysis. Journal of Statistical Software, 32(3), 1--47. URL http://www.jstatsoft.org/v32/i03/.

Examples

library(rrcov)
data(hbk)
hbk.x <- data.matrix(hbk[, 1:3])
CovMMest(hbk.x)

## the following four statements are equivalent
c0 <- CovMMest(hbk.x)
c1 <- CovMMest(hbk.x, bdp = 0.25)
c2 <- CovMMest(hbk.x, control = CovControlMMest(bdp = 0.25))
c3 <- CovMMest(hbk.x, control = new("CovControlMMest", bdp = 0.25))

## direct specification overrides control one:
c4 <- CovMMest(hbk.x, bdp = 0.40,
             control = CovControlMMest(bdp = 0.25))
c1
summary(c1)
plot(c1)

## Deterministic MM-estmates
CovMMest(hbk.x, control=CovControlMMest(sest=CovControlSest(method="sdet")))