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rrcov (version 0.4-01)

CovOgk: Robust Location and Scatter Estimation - Ortogonalized Gnanadesikan-Kettenring (OGK)

Description

Computes a robust multivariate location and scatter estimate with a high breakdown point, using the pairwise algorithm proposed by Marona and Zamar (2002) which in turn is based on the pairwise robust estimator proposed by Gnanadesikan-Kettenring (1972).

Usage

CovOgk(x, niter = 2, beta = 0.9, control)

Arguments

x
a matrix or data frame.
niter
number of iterations, usually 1 or 2 since iterations beyond the second do not lead to improvement.
beta
coverage parameter for the final reweighted estimate
control
a control object (S4) of class CovControlOgk-class containing estimation options - same as these provided in the function specification. If the control object is supplied, the parame

Value

Details

The method proposed by Marona and Zamar (2002) allowes to obtain positive-definite and almost affine equivariant robust scatter matrices starting from any pairwise robust scatter matrix. The default robust estimate of covariance between two random vectors used is the one proposed by Gnanadesikan and Kettenring (1972) but the user can choose any other method by redefining the function in slot vrob of the control object CovControlOgk. Similarly, the function for computing the robust univariate location and dispersion used is the tau scale defined in Yohai and Zamar (1998) but it can be redefined in the control object. The estimates obtained by the OGK method, similarly as in CovMcd are returned as 'raw' estimates. To improve the estimates a reweighting step is performed using the coverage parameter beta and these reweighted estimates are returned as 'final' estimates.

References

Maronna, R.A. and Zamar, R.H. (2002) Robust estimates of location and dispersion of high-dimensional datasets; Technometrics 44(4), 307--317. Yohai, R.A. and Zamar, R.H. (1998) High breakdown point estimates of regression by means of the minimization of efficient scale JASA 86, 403--413. Gnanadesikan, R. and John R. Kettenring (1972) Robust estimates, residuals, and outlier detection with multiresponse data. Biometrics 28, 81--124.

See Also

CovMcd, CovMest

Examples

Run this code
data(hbk)
hbk.x <- data.matrix(hbk[, 1:3])
CovOgk(hbk.x)

## the following three statements are equivalent
c1 <- CovOgk(hbk.x, niter=1)
c2 <- CovOgk(hbk.x, control = CovControlOgk(niter=1))

## direct specification overrides control one:
c3 <- CovOgk(hbk.x, beta=0.95,
             control = CovControlOgk(beta=0.99))
c1


x<-matrix(c(1,2,3,7,1,2,3,7), ncol=2)
##  CovOgk(x)   - this would fail because the two columns of x are exactly collinear.
##              In order to fix it, redefine the default 'vrob' function for example
##              in the following way and pass it as a parameter in the control
##              object.
cc <- CovOgk(x, control=new("CovControlOgk", 
                            vrob=function(x1, x2, ...)
                            {
                                r <- rrcov:::.vrobGK(x1, x2, ...)
                                if(is.na(r))
                                    r <- 0
                                r
                            })
)
cc

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