covMcd {robustbase} | R Documentation |
Compute a robust 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 = NULL, trace = FALSE, use.correction = TRUE, control = rrcov.control())
x |
a matrix or data frame. |
cor |
should the returned result include a correlation matrix?
Default is cor = FALSE |
alpha |
numeric parameter controlling 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 or "best"
or "exact" . Default is nsamp = 500 . For
nsamp = "best" exhaustive enumeration is done, as long as the
number of trials does not exceed 5000. For "exact" ,
exhaustive enumeration will be attempted however many samples are
needed. In this case a warning message will be displayed saying
that the computation can take a very long time. |
seed |
initial seed for random generator, see rrcov.control . |
trace |
logical (or integer) indicating if intermediate results
should be printed; defaults to FALSE ; values >= 2
also produce print from the internal (Fortran) code. |
use.correction |
whether to use finite sample correction
factors; defaults to TRUE . |
control |
a list with estimation options - this includes those
above provided in the function specification, see
rrcov.control for the defaults. If control 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 R function
cov.mcd()
in MASS. The MCD method looks for
the h (> n/2) (h = h(α,n,p) =
h.alpha.n(alpha,n,p)
) 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).
The implementation of covMcd
uses the Fast MCD algorithm of
Rousseeuw and Van Driessen (1999) to approximate the minimum
covariance determinant estimator.
Both rescaling factors (consistency and finite sample) 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 eficiency 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
.
An object of class "mcd"
which is basically 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, with length(best) == quan =
h.alpha.n(alpha,n,p) . |
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. |
cnp2 |
a vector of length two containing the consistency correction factor and the finite sample correction factor of the final estimate of the covariance matrix. |
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. |
raw.cnp2 |
a vector of length two containing the consistency correction factor and the finite sample correction factor of the raw estimate of the covariance matrix. |
X |
the input data as numeric matrix, without NA s. |
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, h, 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). |
call |
the call used (see match.call ). |
Valentin Todorov valentin.todorov@chello.at, based on work written for S-plus by Peter Rousseeuw and Katrien van Driessen from University of Antwerp.
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.
cov.mcd
from package MASS;
covOGK
as cheaper alternative for larger dimensions.
data(hbk) hbk.x <- data.matrix(hbk[, 1:3]) covMcd(hbk.x) ## the following three statements are equivalent c1 <- covMcd(hbk.x, alpha = 0.75) c2 <- covMcd(hbk.x, control = rrcov.control(alpha = 0.75)) ## direct specification overrides control one: c3 <- covMcd(hbk.x, alpha = 0.75, control = rrcov.control(alpha=0.95)) c1