jamestein                package:mcsm                R Documentation

_M_o_n_t_e _C_a_r_l_o _p_l_o_t_s _o_f _t_h_e _r_i_s_k_s _o_f _J_a_m_e_s-_S_t_e_i_n _e_s_t_i_m_a_t_o_r_s

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

     This is a Monte-Carlo representation of the risks of some
     James-Stein estimators of the mean theta of a  _p_-dimensional
     N(theta,I) distribution, taking advantage of a variance reduction
     principle based on recycling random variates.

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

     jamestein(N = 10^3, p = 5)

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

       N: Number of simulations

       p: Dimension of the problem

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

     Given that the risk is computed for all values of the mean theta,
     using a different normal sample for each value of theta creates an
     extraneous noise that is unecessary. Using the same sample
     produces a smooth and well-ordered (in the shrinkage parameter a)
     set of graphs.

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

     Returns a plot with 10 different values of the shrinkage factor a
     between 1 and 2*(p-2), which is the maximal possible value for
     minimaxity.

_W_a_r_n_i_n_g:

     Because of the multiple loops used in the code, this program takes
     quite a while to produce its outcome. Note that there is a
     James-Stein effect only when p>2 but that it may not be  visible
     for a small value of N.

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

     Christian P. Robert and George Casella

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

     Chapter 4 of *EnteR Monte Carlo Statistical Methods*

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

     jamestein(N=2*10^2)     #N is too small to show minimaxity

