rrcov (version 1.7-7)

CovMcd: Robust Location and Scatter Estimation via MCD

Description

Computes a robust multivariate location and scatter estimate with a high breakdown point, using the ‘Fast MCD’ (Minimum Covariance Determinant) estimator.

Usage

CovMcd(x,
       raw.only=FALSE, alpha=control@alpha, nsamp=control@nsamp,
       scalefn=control@scalefn, maxcsteps=control@maxcsteps,
       initHsets=NULL, save.hsets=FALSE,
       seed=control@seed, trace=control@trace,
       use.correction=[e-mail],
       control=CovControlMcd(), ...)

Value

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

Details

This function computes the minimum covariance determinant estimator of location and scatter and returns an S4 object of class CovMcd-class containing the estimates. The implementation of the function is similar to the existing R function covMcd() which returns an S3 object. The MCD method looks for the \(h (> n/2)\) observations (out of \(n\)) whose classical covariance matrix has the lowest possible determinant. The raw MCD estimate of location is then the average of these \(h\) points, whereas the raw MCD estimate of scatter is their covariance matrix, multiplied by a consistency factor and a finite sample correction factor (to make it consistent at the normal model and unbiased at small samples). Both rescaling factors are returned also in the vector raw.cnp2 of length 2. Based on these raw MCD estimates, a reweighting step is performed which increases the finite-sample efficiency considerably - see Pison et al. (2002). The rescaling factors for the reweighted estimates are returned in the vector cnp2 of length 2. Details for the computation of the finite sample correction factors can be found in Pison et al. (2002). The finite sample corrections can be suppressed by setting use.correction=FALSE. The implementation in rrcov uses the Fast MCD algorithm of Rousseeuw and Van Driessen (1999) to approximate the minimum covariance determinant estimator.

References

P. J. Rousseeuw and A. M. Leroy (1987) Robust Regression and Outlier Detection. Wiley.

P. J. Rousseeuw and K. van Driessen (1999) A fast algorithm for the minimum covariance determinant estimator. Technometrics 41, 212--223.

M. Hubert, P. Rousseeuw and T. Verdonck (2012) A deterministic algorithm for robust location and scatter. Journal of Computational and Graphical Statistics 21(3), 618--637.

Pison, G., Van Aelst, S., and Willems, G. (2002), Small Sample Corrections for LTS and MCD, Metrika, 55, 111-123.

Todorov V & Filzmoser P (2009), An Object Oriented Framework for Robust Multivariate Analysis. Journal of Statistical Software, 32(3), 1--47. tools:::Rd_expr_doi("10.18637/jss.v032.i03").

See Also

cov.rob from package MASS

Examples

data(hbk)
hbk.x <- data.matrix(hbk[, 1:3])
CovMcd(hbk.x)
cD <- CovMcd(hbk.x, nsamp = "deterministic")
summary(cD)

## the following three statements are equivalent
c1 <- CovMcd(hbk.x, alpha = 0.75)
c2 <- CovMcd(hbk.x, control = CovControlMcd(alpha = 0.75))
## direct specification overrides control one:
c3 <- CovMcd(hbk.x, alpha = 0.75,
             control = CovControlMcd(alpha=0.95))
c1