Computes a robust multivariate location and scatter estimate with a high breakdown point for incomplete data, using the ‘Fast MCD’ (Minimum Covariance Determinant) estimator.
CovNAMcd(x, alpha = 1/2, nsamp = 500, seed = NULL, trace = FALSE,
use.correction = TRUE, impMeth = c("norm" , "seq", "rseq"), control)An S4 object of class CovNAMcd which is a subclass of the
virtual class CovNARobust.
a matrix or data frame.
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.
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.
starting value for random generator. Default is seed = NULL
whether to print intermediate results. Default is trace = FALSE
whether to use finite sample correction factors.
Default is use.correction=TRUE
select imputation method to use - choose one of "norm" , "seq" or "rseq". The default is "norm"
a control object (S4) of class CovControlMcd-class
containing estimation options - same as these provided in the function
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.
Valentin Todorov valentin.todorov@chello.at
This function computes the minimum covariance determinant estimator
of location and scatter and returns an S4 object of class
CovMcd-class containing the estimates.
The implementation of the function is similar to the existing R function
covMcd() which returns an S3 object.
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 by a consistency factor and a finite sample correction factor
(to make it consistent at the normal model and unbiased at small samples).
Both rescaling factors 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 efficiency 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.
The implementation in rrcov uses the Fast MCD algorithm of Rousseeuw and Van Driessen (1999)
to approximate the minimum covariance determinant estimator.
V. Todorov, M. Templ and P. Filzmoser. Detection of multivariate outliers in business survey data with incomplete information. Advances in Data Analysis and Classification, 5 37--56, 2011.
P. J. Rousseeuw and K. van Driessen (1999) A fast algorithm for the minimum covariance determinant estimator. Technometrics 41, 212--223.
Todorov V & Filzmoser P (2009), An Object Oriented Framework for Robust Multivariate Analysis. Journal of Statistical Software, 32(3), 1--47. <doi:10.18637/jss.v032.i03>.
data(bush10)
mcd <- CovNAMcd(bush10)
mcd
summary(mcd)
plot(mcd)
plot(mcd, which="pairs")
plot(mcd, which="xydistance")
plot(mcd, which="xyqqchi2")
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