cov.rob                 package:MASS                 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(...)
     cov.mcd(...)

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. 

     ...: arguments to 'cov.rob' other than 'method'.

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 (1999) 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. 

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:

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

