covComed function

Co-Median Location and Scatter "Covariance" Estimator

Compute (versions of) the (multivariate) Comedian covariance, i.e., multivariate location and scatter estimator

covComed(X, n.iter = 2, reweight = FALSE, tolSolve = control$tolSolve,
         trace = control$trace, wgtFUN = control$wgtFUN,
         control = rrcov.control())

Arguments

• X: data matrix of dimension, say $n x p$.

• n.iter: number of comedian() iterations. Can be as low as zero.

• reweight: logical indicating if the final distances and weights should be recomputed from the final cov and center. The default is currently FALSE because that was implicit in the first version of the code.

• tolSolve: a numerical tolerance passed to solve.

• trace: logical (or integer) indicating if intermediate results should be printed; defaults to FALSE; values $>= 2$

  also produce print from the internal (Fortran) code.

• wgtFUN: a character string or function, specifying how the weights for the reweighting step should be computed. The default, wgtFUN = "01.original" corresponds to 0-1 weights as proposed originally. Other predefined string options are available, though experimental, see the experimental .wgtFUN.covComed object.

• control: a list with estimation options - this includes those above provided in the function specification, see rrcov.control for the defaults. If control 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.

Details

.. not yet ..

Returns

an object of class "covComed" which is basically a list with components - comp1: Description of 'comp1'

• comp2: Description of 'comp2'

... FIXME ...

References

Falk, M. (1997) On mad and comedians. Annals of the Institute of Statistical Mathematics 49 , 615--644.

Falk, M. (1998). A note on the comedian for elliptical distributions. Journal of Multivariate Analysis 67 , 306--317.

Author(s)

Maria Anna di Palma (initial), Valentin Todorov and Martin Maechler

See Also

covMcd, etc

Examples

data(hbk)
hbk.x <- data.matrix(hbk[, 1:3])
(cc1 <- covComed(hbk.x))
(ccW <- covComed(hbk.x, reweight=TRUE))
cc0  <- covComed(hbk.x, n.iter=0)
cc0W <- covComed(hbk.x, n.iter=0, reweight=TRUE)

stopifnot(all.equal(unclass(cc0), # here, the 0-1 weights don't change:
                    cc0W[names(cc0)], tol=1e-12, check.environment = FALSE),
          which(cc1$weights == 0) == 1:14,
          which(ccW$weights == 0) == 1:14,
          which(cc0$weights == 0) == 1:14)

## Martin's smooth reweighting:

## List of experimental pre-specified wgtFUN() creators:
## Cutoffs may depend on  (n, p, control$beta) :
str(.wgtFUN.covComed)