Abl2               package:pendensity               R Documentation

_C_a_l_c_u_l_a_t_i_n_g _t_h_e _s_e_c_o_n_d _o_r_d_e_r _d_e_r_i_v_a_t_i_v_e _w_i_t_h _a_n_d _w_i_t_h_o_u_t _p_e_n_a_l_t_y

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

     Calculating the second order derivative of the likelihood function
     of the pendensity approach w.r.t. the parameter beta. Thereby, for
     later use, the programm returns the second order derivative with
     and without the penalty.

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

     Abl2(penden.env, lambda0)

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

penden.env: Containing all information, environment of pendensity()

 lambda0: smoothing parameter lambda

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

     We approximate the second order derivative in ths approch with the
     negative fisher information. 

 J(beta)= partial^2 l(beta) / (partial(beta) partial(beta)) = sum(s[i](beta) s[i]^T(beta))

     Therefore we construct the second order derivative of the i-th
     observation w.r.t. beta with the outer product of the matrix
     Abl1.cal and the i-th row of the matrix Abl1.cal.
      The penalty is computed as 

                              lambda Dm

     .

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

Abl2.pen: second order derivative w.r.t. beta with penalty

Abl2.cal: second order derivative w.r.t. beta without penalty. Needed
          for calculating of e.g. AIC.

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

     Christian Schellhase <cschellhase@wiwi.uni-bielefeld.de>

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

     Penalized Density Estimation, Kauermann G. and Schellhase C.
     (2009), to appear.

