scaleTau2             package:robustbase             R Documentation

_R_o_b_u_s_t _T_a_u-_E_s_t_i_m_a_t_e _o_f _S_c_a_l_e

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

     Computes the robust tau-estimate of univariate scale, as proposed
     by Maronna and Zamar (2002); improved by a consistency factor.

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

     scaleTau2(x, c1 = 4.5, c2 = 3.0, consistency = TRUE,
               mu.too = FALSE, ...)

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

       x: numeric vector

   c1,c2: non-negative numbers, specifying cutoff values for the
          biweighting of the mean and the rho function respectively.

  mu.too: logical indicating if both location and scale should be
          returned or just the scale (when 'mu.too=FALSE' as by
          default).

consistency: logical indicating if the consistency correction factor
          (for the scale) should be applied.

     ...: potentially additional arguments which are not used.

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

     First, s0 := MAD, i.e. the equivalent of 'mad(x, constant=1)' is
     computed.  Robustness weights w_i := w_{c1}((x_i - med(X))/ s_0)
     are computed, where w_c(u) = max(0, (1 - (u/c)^2)^2).  The robust
     location measure is defined as mu(X) := (sum_i w_i x_i)/(sum_i
     w_i), and the robust tau-estimate is s(X)^2 := s_0^2 * (1/n) sum_i
     rho_{c2}((x_i - mu(X))/s_0), where rho_c(u) = min(c^2, u^2). 
      'scaleTau2(*, consistency=FALSE)' returns s(X), whereas this
     value is divided by its asymptotic limit when 'consistency = TRUE'
     as by default.

     Note that for 'n = length(x) == 2', all equivariant scale
     estimates are proportional, and specifically, 'scaleTau2(x,
     consistency=FALSE) == mad(x, constant=1)'.  See also the
     reference.

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

     numeric vector of length one (if 'mu.too' is 'FALSE' as by
     default) or two (when 'mu.too = TRUE') with robust scale or
     (location,scale) estimators s^(x) or (m^(x), s^(x)).

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

     Original by Kjell Konis with substantial modifications by Martin
     Maechler.

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

     Maronna, R.A. and Zamar, R.H. (2002) Robust estimates of location
     and dispersion of high-dimensional datasets; _Technometrics_
     *44*(4), 307-317.

_S_e_e _A_l_s_o:

     'Sn', 'Qn', 'mad'; further 'covOGK' for which 'scaleTau2' was
     designed.

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

     x <- c(1:7, 1000)
     sd(x) # non-robust std.deviation
     scaleTau2(x)
     scaleTau2(x, mu.too = TRUE)

