rockem {robust}R Documentation

Contrained M-estimation

Description

Compute a robust estimate of location and scatter using Rocke's contrained M-estimator.

Usage

  rockem(x, control)

Arguments

x a numeric matrix contraining the data.
control a list of control parameters. The utility function covRob.control creates a list of the control parameters and their default values. See details for the required control parameters and their default values.

Details

This function is called by the high-level function covRob when the M-estimator is specified (via the optional argument estim = "m"). It may also be of interest to power users who want to compute a constrained m-estimate with a minimum of fuss.

The required control parameters and their default values are:

quan = 0.5
an integer value giving the number of observations whose covariance determinant will be minimized.
ntrial = 500
a positive integer specifying the number of random trial subsamples that are drawn for large datasets.

The control parameters quan and ntrial are passed to the function fastmcd which computes the initial robust estimate. The remaining parameters affect the constrained m-estimator.

r = 0.45
a numeric value between 0 and 0.5 giving the desired breakdown point.
alpha = 0.05
a numeric value between 0 and 1 specifying the fraction of points receiving zero weight.
tau = 1e-06
a positive numeric value specifying the tolerance used to determine the singularity of the estimated scatter matrix.
tol = 1e-03
a positive numeric value giving the relative precision for the solution of the M-estimate.
maxit = 150
a positive integer specifying the maximum number of m iterations.

Value

a list with the following components:

call an image of the call that produced the object with all the arguments named.
cov a numeric matrix containing the constrained M-estimate of the covariance/correlation matrix.
center a numeric vector containing the constrained M-estimate of the location vector.
raw.cov a numeric matrix containing the initial robust estimate of the covariance/correlation matrix.
raw.center a numeric vector containing the initial robust estimate of the location vector.

References

David M. Rocke (1996). Robustness properties of S-estimators of multivariate location and shape in high dimension. Annals of Statistics, Vol. 24, No. 3, 1327-1345.

See Also

covRob, covRob.control.

Examples

  data(woodmod.dat)
  X <- as.matrix(woodmod.dat)
  m.control <- covRob.control("m")
  rockem(X, m.control)

[Package robust version 0.3-0 Index]