MM Estimates of Multivariate Location and Scatter

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Description

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

Usage

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

Value

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

Author(s)

Valentin Todorov valentin.todorov@chello.at

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

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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")))

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