fg1                 package:CVThresh                 R Documentation

_f_g_1 _f_u_n_c_t_i_o_n

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

     This function generates fg1 function values for n equally spaced
     points in [0,1].

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

     fg1(n=1024)

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

       n: the number of data

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

     A smooth function fg1 is introduced by Fan and Gijbels (1995) and
     is useful test function evaluating a wavelet shrinkage method.

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

     fg1 function values f(i/n), i=1,...,n and its variability ||f|| =
     sum_{i=1}^n (f_i - mena(f))^2 / (n-1) where mena(f) = sum_{i=1}^n
     f_i / n.

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

     Fan, J. and Gijbels, I. (1995)  Data-driven bandwidth selection in
     local polynomial fitting: Variable bandwidth and spatial
     adaptation. _Journal of the Royal Statistical Society Ser. B_
     *57*, 371-394.

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

     'dopp', 'heav', 'poly'.

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

     testfg1 <- fg1(1024)
     plot(testfg1$x, testfg1$meanf, xlab="", ylab="", 
          main="Plot of fg1 function", type="l")

