Computes constrained M-Estimates of multivariate location and scatter
based on the translated biweight function (‘t-biweight’) using
a High breakdown point initial estimate. The default initial estimate
is the Minimum Volume Ellipsoid computed
with CovMve. The raw (not reweighted) estimates are taken
and the covariance matrix is standardized to determinant 1.
covMest(x, cor=FALSE, r = 0.45, arp = 0.05, eps=1e-3,
maxiter=120, control, t0, S0)An object of class "mest" which is basically a list with
the following components. This class is "derived" from "mcd" so that
the same generic functions - print, plot, summary - can
be used.
NOTE: this is going to change - in one of the next revisions covMest
will return an S4 class "mest" which is derived (i.e. contains)
form class "cov".
the final estimate of location.
the final estimate of scatter.
the estimate of the correlation matrix (only if
cor = TRUE).
mahalanobis distances of the observations using the M-estimate of the location and scatter.
the input data as a matrix.
total number of observations.
character string naming the method (M-Estimates).
the call used (see match.call).
a matrix or data frame.
should the returned result include a correlation matrix?
Default is cor = FALSE
.
required breakdown point. Allowed values are between
(n - p)/(2 * n) and 1 and the default is 0.45
asympthotic rejection point, i.e. the fraction of points
receiving zero weight (see Rocke (1996)). Default is 0.05.
a numeric value specifying the relative precision of the solution of
the M-estimate. Defaults to 1e-3
maximum number of iterations allowed in the computation of the M-estimate. Defaults to 120
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.
optional initial high breakdown point estimates of the location. If not supplied MVE will be used.
optional initial high breakdown point estimates of the scatter. If not supplied MVE will be used.
Valentin Todorov valentin.todorov@chello.at,
(some code from C. Becker - http://www.sfb475.uni-dortmund.de/dienst/de/content/struk-d/bereicha-d/tpa1softw-d.html)
Rocke (1996) has shown that the S-estimates of multivariate location and scatter
in high dimensions can be sensitive to outliers even if the breakdown point
is set to be near 0.5. To mitigate this problem he proposed to utilize
the translated biweight (or t-biweight) method with a
standardization step consisting of equating the median of rho(d)
with the median under normality. This is then not an S-estimate, but is
instead a constrained M-estimate. In order to make the smooth estimators
to work, a reasonable starting point is necessary, which will lead reliably to a
good solution of the estimator. In covMest the MVE computed by
CovMve is used, but the user has the possibility to give her own
initial estimates.
D.L.Woodruff and D.M.Rocke (1994) Computable robust estimation of multivariate location and shape on high dimension using compound estimators, Journal of the American Statistical Association, 89, 888--896.
D.M.Rocke (1996) Robustness properties of S-estimates of multivariate location and shape in high dimension, Annals of Statistics, 24, 1327-1345.
D.M.Rocke and D.L.Woodruff (1996) Identification of outliers in multivariate data Journal of the American Statistical Association, 91, 1047--1061.
Todorov V & Filzmoser P (2009), An Object Oriented Framework for Robust Multivariate Analysis. Journal of Statistical Software, 32(3), 1--47. tools:::Rd_expr_doi("10.18637/jss.v032.i03").
covMcd