Resistant Estimation of Multivariate Location and Scatter

Usage

cov.rob(x, cor=FALSE, quantile.used=floor((n + p + 1)/2),
        method=c("mve", "mcd", "classical"), nsamp="best", seed)
cov.mve(x, cor=FALSE, quantile.used=floor((n + p + 1)/2),
        nsamp="best", seed)
cov.mcd(x, cor=FALSE, quantile.used=floor((n + p + 1)/2),
        nsamp="best", seed)

Arguments

x a matrix or data frame.
cor should the returned result include a correlation matrix?
quantile.used the minimum number of the data points regarded as good points.
method the method to be used – minimum volume ellipsoid, minimum covariance determinant or classical product-moment. Using cov.mve or cov.mcd forces mve or mcd respectively.
nsamp the number of samples or "best" or "exact" or "sample". If "sample" the number chosen is min(5*p, 3000), taken from Rousseeuw and Hubert (1997). If "best" exhaustive enumeration is done up to 5000 samples: if "exact" exhaustive enumeration will be attempted however many samples are needed.
seed the seed to be used for random sampling: see RNGkind. The current value of .Random.seed will be preserved if it is set.

Description

Compute a multivariate location and scale estimate with a high breakdown point – this can be thought of as estimating the mean and covariance of the good part of the data. cov.mve and cov.mcd are compatibility wrappers.

Details

For method "mve", an approximate search is made of a subset of size quantile.used with an enclosing ellipsoid of smallest volume; in method "mcd" it is the volume of the Gaussian confidence ellipsoid, equivalently the determinant of the classical covariance matrix, that is minimized. The mean of the subset provides a first estimate of the location, and the rescaled covariance matrix a first estimate of scatter. The Mahalanobis distances of all the points from the location estimate for this covariance matrix are calculated, and those points within the 97.5% point under Gaussian assumptions are declared to be good. The final estimates are the mean and rescaled covariance of the good points.

The rescaling is by the appropriate percentile under Gaussian data; in addition the first covariance matrix has an ad hoc finite-sample correction given by Marazzi.

For method "mve" the search is made over ellipsoids determined by the covariance matrix of p of the data points. For method "mcd" an additional improvement step suggested by Rousseeuw and van Driessen (1997) is used, in which once a subset of size quantile.used is selected, an ellipsoid based on its covariance is tested (as this will have no larger a determinant, and may be smaller).

Value

A list with components

center the final estimate of location.
cov the final estimate of scatter.
cor (only is cor=TRUE) the estimate of the correlation matrix.
sing message giving number of singular samples out of total
crit the value of the criterion on log scale. For MCD this is the determinant, and for MVE it is proportional to the volume.
best the subset used. For MVE the best sample, for MCD the best set of size quantile.used.
n.obs total number of observations.

Author(s)

B.D. Ripley

References

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

A. Marazzi (1993) Algorithms, Routines and S Functions for Robust Statistics. Wadsworth and Brooks/Cole.

P. J. Rousseeuw and B. C. van Zomeren (1990) Unmasking multivariate outliers and leverage points, Journal of the American Statistical Association, 85, 633-639.

P. J. Rousseeuw and K. van Driessen (1997) A fast algorithm for the minimum covariance determinant estimator. Technical Report, Department of Mathematics and Computer Science, Universitaire Instelling Antwerpen.

See Also

lqs

Examples

data(stackloss)
.Random.seed <- 1:4
cov.rob(stackloss)
cov.rob(stack.x, method="mcd", nsamp="exact")

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