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, control)
x |
a matrix or data frame. |
cor |
should the returned result include a correlation matrix? Default is cor = FALSE |
alpha |
This parameter controls the size of the subsets over which the determinant is
minimized, i.e. alpha*n observations are used for computing the determinant. Allowed values are between 0.5 and 1 and the default is 0.5. |
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 |
control |
a list with 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. |
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 finite-sample 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 scatter. |
mcd.wt |
weights of the observations using the final estimate of the location and scatter. |
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 scatter. |
raw.weights |
weights of the observations based on the raw estimate of the location and scatter. |
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, 111-123.
data(hbk) covMcd(hbk.x) # the following three statements are equivalent covMcd(hbk.x, alpha=0.75) covMcd(hbk.x, control = rrcov.control(alpha=0.75)) covMcd(hbk.x, alpha = 0.75, control = rrcov.control(alpha=0.95))