covMcd                 package:rrcov                 R Documentation

_R_o_b_u_s_t _l_o_c_a_t_i_o_n _a_n_d _s_c_a_t_t_e_r _e_s_t_i_m_a_t_i_o_n _w_i_t_h _h_i_g_h _b_r_e_a_k_d_o_w_n _p_o_i_n_t

_D_e_s_c_r_i_p_t_i_o_n:

     Compute a multivariate location and scale estimate with a high
     breakdown point using the Fast MCD (Minimum Covariance
     Determinant) Estimator.

_U_s_a_g_e:

     covMcd(x, cor=FALSE, alpha=1/2, nsamp=500, seed=0, print.it=FALSE, use.correction=TRUE, control)

_A_r_g_u_m_e_n_t_s:

       x: a matrix or data frame. 

     cor: should the returned result include a correlation matrix?
          Default is 'cor = FALSE' 

   alpha: This parameter controls the size of the subsets over which
          the  determinant is minimized, i.e. 'alpha*n' observations
          are used  for computing the determinant. Allowed values are
          between 0.5 and 1 and the default is 0.5.  

   nsamp: number of subsets used for initial estimates or '"best"'  or
          '"exact"'. Default is 'nsamp = 500'.  If 'nsamp="best"'
          exhaustive enumeration is done, as far as the number of
          trials do not exceed 5000. If 'nsamp="exact"' exhaustive
          enumeration will be attempted however many samples are
          needed.  In this case a warning message will be displayed
          saying that the computation can take a very long time. 

    seed: starting value for random generator. Default is 'seed = 0'

print.it: whether to print intermediate results. Default is 'print.it =
          FALSE'

use.correction: whether to use finite sample correction factors.
          Default is 'use.correction=TRUE'

 control: a list with estimation options - same as these provided in
          the  fucntion 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. 

_D_e_t_a_i_l_s:

     This function computes the minimum covariance determinant
     estimator of location and scatter. The MCD method looks for the
     h(> n/2) observations (out of n) whose classical covariance 
     matrix has the lowest possible determinant. The raw MCD estimate 
     of location is then the average of these h points, whereas the raw
     MCD  estimate of scatter is their covariance matrix, multiplied
     with a consistency factor and a finite sample correction factor.
     Both rescaling factors are  returned also in the vector 'raw.cnp2'
     of length 2. Based on these raw MCD estimates, a reweighting step
     is performed which increases the finite-sample eficiency
     considerably - see Pison et.al. (2002).  The rescaling factors for
     the reweighted estimates are returned in the vector 'cnp2' of
     length 2.  Details for the computation of the finite sample
     correction factors can be found in Pison et.al. (2002).  The
     finite sample corrections can be suppressed by setting
     'use.correction=FALSE'. The implementation in rrcov uses the Fast
     MCD algorithm of Rousseeuw and Van Driessen (1999) to approximate
     the minimum covariance determinant estimator.

_V_a_l_u_e:

     A list with components

  center: the final estimate of location. 

     cov: the final estimate of scatter. 

     cor: the (final) estimate of the correlation matrix (only if 'cor
          = TRUE') . 

    crit: the value of the criterion, i.e. the determinant. 

    best: the best subset found and used for computing the raw
          estimates. The size of 'best' is equal to 'quan'. 

     mah: mahalanobis distances of the observations using the final
          estimate of the location and scatter. 

  mcd.wt: weights of the observations using the final estimate of the
          location and scatter. 

    cnp2: a vector of length two containing the consistency correction
          factor and the  finite sample correction factor of the final
          estimate of the covariance matrix. 

raw.center: the raw (not reweighted) estimate of location. 

 raw.cov: the raw (not reweighted) estimate of scatter. 

 raw.mah: mahalanobis distances of the observations based on the raw
          estimate of the location and scatter. 

raw.weights: weights of the observations based on the raw estimate of
          the location and scatter. 

raw.cnp2: a vector of length two containing the consistency correction
          factor and the  finite sample correction factor of the raw
          estimate of the covariance matrix. 

       X: the input data as a matrix. 

   n.obs: total number of observations.  

   alpha: the size of the subsets over which the determinant is
          minimized (the default is (n+p+1)/2).  

    quan: the number of observations on which the MCD is based.  If
          'quan' equals 'n.obs', the MCD is the classical covariance
          matrix. 

  method: character string naming the method (Minimum Covariance
          Determinant). 

_R_e_f_e_r_e_n_c_e_s:

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

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

     Pison, G., Van Aelst, S., and Willems, G. (2002),  Small Sample
     Corrections for LTS and MCD,  _Metrika_, *55*, 111-123.

_E_x_a_m_p_l_e_s:

     data(hbk)
     covMcd(hbk.x)

     # the following three statements are equivalent
     covMcd(hbk.x, alpha=0.75)
     covMcd(hbk.x, control = rrcov.control(alpha=0.75))
     covMcd(hbk.x, alpha = 0.75, control = rrcov.control(alpha=0.95))

