Computes a robust multivariate location and scatter estimate with a high breakdown point for incomplete data, using the pairwise algorithm proposed by Marona and Zamar (2002) which in turn is based on the pairwise robust estimator proposed by Gnanadesikan-Kettenring (1972).
CovNAOgk(x, niter = 2, beta = 0.9, impMeth = c("norm" , "seq", "rseq"), control)An S4 object of class CovNAOgk which is a subclass of the
virtual class CovNARobust.
a matrix or data frame.
number of iterations, usually 1 or 2 since iterations beyond the second do not lead to improvement.
coverage parameter for the final reweighted estimate
select imputation method to use - choose one of "norm" , "seq" or "rseq". The default is "norm"
a control object (S4) of class CovControlOgk-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. The control
object contains also functions for computing the robust univariate location
and dispersion estimate mrob and for computing the robust estimate
of the covariance between two random variables vrob.
Valentin Todorov valentin.todorov@chello.at
The method proposed by Marona and Zamar (2002) allowes to obtain
positive-definite and almost affine equivariant robust scatter matrices
starting from any pairwise robust scatter matrix. The default robust estimate
of covariance between two random vectors used is the one proposed by
Gnanadesikan and Kettenring (1972) but the user can choose any other method by
redefining the function in slot vrob of the control object
CovControlOgk. Similarly, the function for computing the robust
univariate location and dispersion used is the tau scale defined
in Yohai and Zamar (1998) but it can be redefined in the control object.
The estimates obtained by the OGK method, similarly as in CovMcd are returned
as 'raw' estimates. To improve the estimates a reweighting step is performed using
the coverage parameter beta and these reweighted estimates are returned as
'final' estimates.
Yohai, R.A. and Zamar, R.H. (1998) High breakdown point estimates of regression by means of the minimization of efficient scale JASA 86, 403--413.
Gnanadesikan, R. and John R. Kettenring (1972) Robust estimates, residuals, and outlier detection with multiresponse data. Biometrics 28, 81--124.
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>.
CovNAMcd
data(bush10)
CovNAOgk(bush10)
## the following three statements are equivalent
c1 <- CovNAOgk(bush10, niter=1)
c2 <- CovNAOgk(bush10, control = CovControlOgk(niter=1))
## direct specification overrides control one:
c3 <- CovNAOgk(bush10, beta=0.95,
control = CovControlOgk(beta=0.99))
c1
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