cov.rob                 package:lqs                 R Documentation

Resistant Estimation of Multivariate Location and Scatter

Description:

     Compute a multivariate location and scale estimate with a high
     breakdown point - this can be thought of as estimating the mean
     and covariance of the `good' part of the data. `cov.mve' and
     `cov.mcd' are compatibility wrappers.

Usage:

     cov.rob(x, cor = FALSE, quantile.used = floor((n + p + 1)/2),
             method = c("mve", "mcd", "classical"), nsamp = "best", seed)
     cov.mve(x, cor = FALSE, quantile.used = floor((n + p + 1)/2),
             nsamp = "best", seed)
     cov.mcd(x, cor = FALSE, quantile.used = floor((n + p + 1)/2),
             nsamp = "best", seed)

Arguments:

       x: a matrix or data frame. 

     cor: should the returned result include a correlation matrix? 

quantile.used: the minimum number of the data points regarded as `good'
          points. 

  method: the method to be used - minimum volume ellipsoid, minimum
          covariance determinant or classical product-moment. Using
          `cov.mve' or `cov.mcd' forces `mve' or `mcd' respectively. 

   nsamp: the number of samples or `"best"' or `"exact"' or `"sample"'.
          If `"sample"' the number chosen is `min(5*p, 3000)', taken
          from Rousseeuw and Hubert (1997). If `"best"' exhaustive
          enumeration is done up to 5000 samples: if `"exact"'
          exhaustive enumeration will be attempted however many samples
          are needed. 

    seed: the seed to be used for random sampling: see `RNGkind'. The
          current value of `.Random.seed' will be preserved if it is
          set. 

Details:

     For method `"mve"', an approximate search is made of a subset of
     size `quantile.used' with an enclosing ellipsoid of smallest
     volume; in method `"mcd"' it is the volume of the Gaussian
     confidence ellipsoid, equivalently the determinant of the
     classical covariance matrix, that is minimized. The mean of the
     subset provides a first estimate of the location, and the rescaled
     covariance matrix a first estimate of scatter. The Mahalanobis
     distances of all the points from the location estimate for this
     covariance matrix are calculated, and those points within the
     97.5% point under Gaussian assumptions are declared to be `good'.
     The final estimates are the mean and rescaled covariance of the
     `good' points.

     The rescaling is by the appropriate percentile under Gaussian
     data; in addition the first covariance matrix has an ad hoc
     finite-sample correction given by Marazzi.

     For method `"mve"' the search is made over ellipsoids determined
     by the covariance matrix of `p' of the data points. For method
     `"mcd"' an additional improvement step suggested by Rousseeuw and
     van Driessen (1997) is used, in which once a subset of size
     `quantile.used' is selected, an ellipsoid based on its covariance
     is tested (as this will have no larger a determinant, and may be
     smaller).

Value:

     A list with components

  center: the final estimate of location. 

     cov: the final estimate of scatter. 

     cor: (only is `cor = TRUE') the estimate of the correlation
          matrix. 

    sing: message giving number of singular samples out of total 

    crit: the value of the criterion on log scale. For MCD this is the
          determinant, and for MVE it is proportional to the volume. 

    best: the subset used. For MVE the best sample, for MCD the best
          set of size `quantile.used'. 

   n.obs: total number of observations. 

Author(s):

     B.D. Ripley

References:

     P. J. Rousseeuw and A. M. Leroy (1987)  Robust Regression and
     Outlier Detection. Wiley.

     A. Marazzi (1993)  Algorithms, Routines and S Functions for Robust
     Statistics. Wadsworth and Brooks/Cole. 

     P. J. Rousseeuw and B. C. van Zomeren (1990) Unmasking
     multivariate outliers and leverage points,  Journal of the
     American Statistical Association, 85, 633-639.

     P. J. Rousseeuw and K. van Driessen (1999) A fast algorithm for
     the minimum covariance determinant estimator. Technometrics 41,
     212-223.

     P. Rousseeuw and M. Hubert (1997) Recent developments in PROGRESS.
     In L1-Statistical Procedures and Related Topics  ed Y. Dodge, IMS
     Lecture Notes volume 31, pp. 201-214.

See Also:

     `lqs'

Examples:

     data(stackloss)
     set.seed(123)
     cov.rob(stackloss)
     cov.rob(stack.x, method = "mcd", nsamp = "exact")

