tukeyChi             package:robustbase             R Documentation

_T_u_k_e_y'_s "_C_h_i", _t_h_e _B_i-_s_q_u_a_r_e _L_o_s_s (_R_h_o) _F_u_n_c_t_i_o_n

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

     Computes Tukey's bi-square loss function, 'chi(x)' and its first
     two derivatives.  Note that in the general context of
     M-estimators, these loss functions are called rho-functions.

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

     tukeyChi(x, cc, deriv = 0)

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

       x: numeric vector.

      cc: tuning constant 

   deriv: integer in {0,1,2} specifying the order of the derivative;
          the default, 'deriv = 0' computes the chi- (or rho-)function.

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

     a numeric vector of the same length as 'x'.

_N_o_t_e:

     'tukeyChi(x, d)' and 'tukeyPsi1(x, d-1)' are just re-scaled
     versions of each other (for 'd in 0:2').

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

     Matias Salibian-Barrera and Martin Maechler

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

     'lmrob' and 'tukeyPsi1'.

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

     op <- par(mfrow = c(3,1), oma = c(0,0, 2, 0),
               mgp = c(1.5, 0.6, 0), mar= .1+c(3,4,3,2))
     x <- seq(-2.5, 2.5, length = 201)
     cc <- 1.55 # as set by default in lmrob.control()
     plot. <- function(...) { plot(...); abline(h=0,v=0, col="gray", lty=3)}
     plot.(x, tukeyChi(x, cc), type = "l", col = 2)
     plot.(x, tukeyChi(x, cc, deriv = 1), type = "l", col = 2)
     plot.(x, tukeyChi(x, cc, deriv = 2), type = "l", col = 2)
     mtext(sprintf("tukeyChi(x, c = %g, deriv),  deriv = 0,1,2", cc),
           outer = TRUE, font = par("font.main"), cex = par("cex.main"))
     par(op)

