covMcd {rrcov}  R Documentation 
Compute a multivariate location and scale estimate with a high breakdown point using the Fast MCD (Minimum Covariance Determinant) Estimator.
covMcd(x, cor=FALSE, alpha=1/2, nsamp=500, seed=0, print.it=FALSE)
x 
a matrix or data frame. 
cor 
should the returned result include a correlation matrix? Default is cor = FALSE 
alpha 
The size of the subsets over which the determinant is minimized. Must be between the default = (n+p+1)/2 and n. Provide a fraction between .5 and 1, indicating the fraction of the data over which the determinant is minimized. 
nsamp 
number of subsets used for initial estimates. Default is nsamp = 500 
seed 
starting value for random generator. Default is seed = 0 
print.it 
whether to print intermediate results. Default is print.it = FALSE 
The minimum covariance determinant estimator of location and scatter implemented in covMcd() is similar to the existing R function cov.mcd() in MASS. 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 with a consistency factor. Based on these raw MCD estimates, a reweighting step is performed which increases the finitesample eficiency considerably  see Pison et.al. (2002). The implementation in rrcov uses the Fast MCD algorithm of Rousseeuw and Van Driessen (1999) to approximate the minimum covariance determinant estimator.
A list with components
center 
the final estimate of location. 
cov 
the final estimate of scatter. 
cor 
the (final) estimate of the correlation matrix (only if cor = TRUE ) .

crit 
the value of the criterion, i.e. the determinant. 
best 
the best subset found and used for computing the raw estimates. The size of best is equal to quan .

mah 
mahalanobis distances of the observations using the final estimate of the location and scater. 
mcd.wt 
weights of the observations using the final estimate of the location and scater. 
raw.center 
the raw (not reweighted) estimate of location. 
raw.cov 
the raw (not reweighted) estimate of scatter. 
raw.mah 
mahalanobis distances of the observations based on the raw estimate of the location and scater. 
raw.weights 
weights of the observations based on the raw estimate of the location and scater. 
X 
the input data as a matrix. 
n.obs 
total number of observations. 
alpha 
the size of the subsets over which the determinant is minimized (the default is (n+p+1)/2). 
quan 
the number of observations on which the MCD is based.
If quan equals n.obs , the MCD is the classical covariance matrix.

method 
character string naming the method (Minimum Covariance Determinant). 
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.
Pison, G., Van Aelst, S., and Willems, G. (2002), Small Sample Corrections for LTS and MCD, Metrika, 55, 111123.
data(hbk) covMcd(hbk.x)