akj                 package:quantreg                 R Documentation

_D_e_n_s_i_t_y _e_s_t_i_m_a_t_i_o_n _u_s_i_n_g _a_d_a_p_t_i_v_e _k_e_r_n_e_l _m_e_t_h_o_d

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

     univariate adaptive kernel density estimation a la Silverman.  As
     used by Portnoy and Koenker (1989)

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

     akj(x, z, p, h, alpha, kappa, iker1, iker2)

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

       x: points used for centers of kernel assumed to be sorted

       z: points at which density is calculated; default to seq(
          min(x), max(x), 2*length(x) )

       p: vector of probabilities associated with x's; default to
          1/len(x) for each x.

       h: initial window size (overall); default to Silverman's normal
          reference

   alpha: a sensitivity parameter that determines the sensitivity of
          the local bandwidth to variations in the pilot density;
          default to .5

   kappa: constant determining initial (default) window width

   iker1: kernel indicator, 0 for normal kernel (default) while 1 for
          cauchy kernel

   iker2: xxx

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

     a R structure is returned

    dens: the vector of estimated density

     psi: a vector of psi=-f'/f function

   score: a vector of score (f'/f)^2-f''/f function

       h: same as the input argument h

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

     Portnoy, S and R Koenker, (1989) Adaptive L Estimation of Linear
     Models, Annals, 17, 362-81. Silverman, B. (1986) Density
     Estimation, pp100-104.

