shorth                package:parody                R Documentation

_o_n_e-_d_i_m_e_n_s_i_o_n_a_l _M_V_E (_m_i_n. _v_o_l. _e_l_l_i_p_s_o_i_d)

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

     generalized length of shortest-half sample

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

     shorth(x, Alpha=0.5)

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

       x: data vector, no NAs 

   Alpha: minimum fraction of data to be covered by scale estimator. if
          Alpha == 0.5, the 'shorth' is calculated 

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

     a list, say L, with components 

  shorth: a 2-vector with endpoints of the shortest Alpha-sample 

length.shorth: see previous return component 'L$shorth[2]-L$shorth[1]' 

midpt.shorth: mean(L[["shorth"]]) 

meanshorth: mean of values in the shorth, studied by Andrews et al
          (1972) as a location estimator 

correction.parity.dep: correction factor to be applied to achieve
          approximate unbiasedness and diminish small-sample parity
          dependence; 'L["shorth"]] * L[["correction"]]' is
          approximately unbiased for the Gaussian standard deviation,
          for 0 < Alpha < 1. 

bias.correction.gau.5: correction factor to be applied along with
          correction.parity.dep when Alpha = .5; empirically derived
          bias correction useful for 10 < N < 2000 and possibly beyond.
           To use, divide:  '(L[["shorth"]] * L[["correction"]] /
          L[["bias.corr"]])' is approximately unbiased for Gaussian
          standard deviation, when Alpha=.5. 

   Alpha: coverage fraction used 

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

     Rousseeuw and Leroy, Stat Neer (1988), Gruebel, Ann Stat (1988)

