Robust Location and Scatter Estimation via MVE
Computes a robust multivariate location and scatter estimate with a high breakdown point, using the ‘MVE’ (Minimum Volume Ellipsoid) estimator.
CovMve(x, alpha = 1/2, nsamp = 500, seed = NULL, trace = FALSE, control)
x |
a matrix or data frame. |
alpha |
numeric parameter controlling the size of the subsets
over which the determinant is minimized, i.e., |
nsamp |
number of subsets used for initial estimates or |
seed |
starting value for random generator. Default is |
trace |
whether to print intermediate results. Default is |
control |
a control object (S4) of class |
This function computes the minimum volume ellipsoid estimator
of location and scatter and returns an S4 object of class
CovMve-class containing the estimates.
The approximate estimate is
based on a subset of size alpha*n with an enclosing ellipsoid of smallest volume.
The mean of the best found subset provides the raw estimate of the location,
and the rescaled covariance matrix is the raw estimate of scatter. The rescaling of
the raw covariance matrix is by median(dist)/qchisq(0.5, p) and this scale factor
is returned in the slot raw.cnp2. Currently no finite sample corrction factor is applied.
The Mahalanobis distances of all observations from the location estimate for the
raw covariance matrix are calculated, and those points within the 97.5
under Gaussian assumptions are declared to be good. The final (reweightd) estimates are the
mean and rescaled covariance of the good points. The reweighted covariance matrix is
rescaled by 1/pgamma(qchisq(alpha, p)/2, p/2 + 1)/alpha
(see Croux and Haesbroeck, 1999) and this scale factor is returned
in the slot cnp2.
The search for the approximate solution is made over ellipsoids determined by the
covariance matrix of p+1 of the data points and applying
a simple but effective improvement of the subsampling procedure
as described in Maronna et al. (2006), p. 198.
Although there exists no formal proof of this improvement (as for MCD and LTS),
simulations show that it can be recommended as an approximation of the MVE.
An S4 object of class CovMve-class which is a subclass of the
virtual class CovRobust-class.
Main reason for implementing the MVE estimate was that it is the recommended
initial estimate for S estimation (see Maronna et al. (2006), p. 199) and will
be used by default in CovMest (after removing the correction
factors from the covariance matrix and rescaling to determinant 1).
Valentin Todorov valentin.todorov@chello.at and Matias Salibian-Barrera matias@stat.ubc.ca
P. J. Rousseeuw and A. M. Leroy (1987) Robust Regression and Outlier Detection. Wiley.
C. Croux and G. Haesbroeck (1999). Influence function and efficiency of the minimum covariance determinant scatter matrix estimator. Journal of Multivariate Analysis, 71, 161–190.
R. A. Maronna, D. Martin and V. Yohai (2006). Robust Statistics: Theory and Methods. Wiley, New York.
Todorov V & Filzmoser P (2009), An Object Oriented Framework for Robust Multivariate Analysis. Journal of Statistical Software, 32(3), 1–47. URL http://www.jstatsoft.org/v32/i03/.
cov.rob from package MASS
data(hbk)
hbk.x <- data.matrix(hbk[, 1:3])
CovMve(hbk.x)
## the following three statements are equivalent
c1 <- CovMve(hbk.x, alpha = 0.75)
c2 <- CovMve(hbk.x, control = CovControlMve(alpha = 0.75))
## direct specification overrides control one:
c3 <- CovMve(hbk.x, alpha = 0.75,
control = CovControlMve(alpha=0.95))
c1Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.