arw                  package:StatDA                  R Documentation

_A_d_a_p_t_i_v_e _r_e_w_e_i_g_h_t_e_d _e_s_t_i_m_a_t_o_r _f_o_r _m_u_l_t_i_v_a_r_i_a_t_e _l_o_c_a_t_i_o_n _a_n_d _s_c_a_t_t_e_r

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

     Adaptive reweighted estimator for multivariate location and
     scatter with hard-rejection weights.  The multivariate outliers
     are defined  according to the supremum of the difference between
     the empirical distribution function of the robust Mahalanobis
     distance and the  theoretical distribution function.

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

     arw(x, m0, c0, alpha, pcrit)

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

       x: Dataset (n x p)

      m0: Initial location estimator (1 x p)

      c0: Initial scatter estimator (p x p)

   alpha: Maximum thresholding proportion (optional scalar, default:
          alpha = 0.025)

   pcrit: Critical value obtained by simulations (optional scalar,
          default value obtained from simulations)

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

     At the basis of initial estimators of location and scatter, the
     function arw  performs a reweighting step to adjust the threshold
     for outlier rejection.  The critical value pcrit was obtained by
     simulations using the MCD estimator as initial robust covariance
     estimator. If a different estimator is used, pcrit should be
     changed and computed by simulations for the specific dimensions of
     the data x.

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

       m: Adaptive location estimator (p x 1)

       c: Adaptive scatter estimator (p x p)

      cn: Adaptive threshold ("adjusted quantile")

       w: Weight vector (n x 1)

_A_u_t_h_o_r(_s):

     Moritz Gschwandtner <e0125439@student.tuwien.ac.at> 
      Peter Filzmoser <P.Filzmoser@tuwien.ac.at> <URL:
     http://www.statistik.tuwien.ac.at/public/filz/>

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

     P. Filzmoser, R.G. Garrett, and C. Reimann (2005). Multivariate
     outlier detection in exploration geochemistry. _Computers &
     Geosciences_.

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

     x <- cbind(rnorm(100), rnorm(100))
     arw(x, apply(x,2,mean), cov(x))

