Stahel-Donoho Estimates of Multivariate Location and Scatter
Compute a robust estimate of location and scale using the Stahel-Donoho projection based estimator
CovSde(x, nsamp, maxres, tune = 0.95, eps = 0.5, prob = 0.99, seed = NULL, trace = FALSE, control)
x |
a matrix or data frame. |
nsamp |
a positive integer giving the number of resamples required;
|
maxres |
a positive integer specifying the maximum number of
resamples to be performed including those that are discarded due to linearly
dependent subsamples. If |
tune |
a numeric value between 0 and 1 giving the fraction of the data to receive non-zero weight.
Defaults to |
prob |
a numeric value between 0 and 1 specifying the probability of high breakdown point;
used to compute |
eps |
a numeric value between 0 and 0.5 specifying the breakdown point; used to compute
|
seed |
starting value for random generator. Default is |
trace |
whether to print intermediate results. Default is |
control |
a control object (S4) of class |
The projection based Stahel-Donoho estimator posses very good statistical properties,
but it can be very slow if the number of variables is too large. It is recommended to use
this estimator if n <= 1000 and p<=10 or n <= 5000 and p<=5.
The number of subsamples required is calculated to provide a breakdown point of
eps with probability prob and can reach values larger than
the larger integer value - in such case it is limited to .Machine$integer.max.
Of course you could provide nsamp in the call, i.e. nsamp=1000 but
this will not guarantee the required breakdown point of th eestimator.
For larger data sets it is better to use CovMcd or CovOgk.
If you use CovRobust, the estimator will be selected automatically
according on the size of the data set.
An S4 object of class CovSde-class which is a subclass of the
virtual class CovRobust-class.
The Fortran code for the Stahel-Donoho method was taken almost with no changes from
package robust which in turn has it from the Insightful Robust Library
(thanks to by Kjell Konis).
Valentin Todorov valentin.todorov@chello.at and Kjell Konis kjell.konis@epfl.ch
R. A. Maronna and V.J. Yohai (1995) The Behavior of the Stahel-Donoho Robust Multivariate Estimator. Journal of the American Statistical Association 90 (429), 330–341.
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/.
data(hbk)
hbk.x <- data.matrix(hbk[, 1:3])
CovSde(hbk.x)
## the following four statements are equivalent
c0 <- CovSde(hbk.x)
c1 <- CovSde(hbk.x, nsamp=2000)
c2 <- CovSde(hbk.x, control = CovControlSde(nsamp=2000))
c3 <- CovSde(hbk.x, control = new("CovControlSde", nsamp=2000))
## direct specification overrides control one:
c4 <- CovSde(hbk.x, nsamp=100,
control = CovControlSde(nsamp=2000))
c1
summary(c1)
plot(c1)
## Use the function CovRobust() - if no estimation method is
## specified, for small data sets CovSde() will be called
cr <- CovRobust(hbk.x)
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