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)

_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: The size of the subsets over which the determinant is
          minimized. Must be between the default = (n+p+1)/2 and n.
          Provide a fraction between .5 and 1, indicating the fraction
          of the data over which the determinant is minimized. 

   nsamp: number of subsets used for initial estimates. Default is
          'nsamp = 500'

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

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

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

     The minimum covariance determinant estimator of location and
     scatter implemented in covMcd() is similar to the existing  R
     function cov.mcd() in MASS. 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. Based on these raw MCD estimates, a
     reweighting step is performed which increases the finite-sample
     eficiency considerably - see Pison et.al. (2002).  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 scater. 

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

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 scater. 

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

       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)

