lspline                package:assist                R Documentation

_C_a_l_c_u_l_a_t_e _R_e_p_r_o_d_u_c_i_n_g _K_e_r_n_e_l_s _f_o_r _S_o_m_e _L-_s_p_l_i_n_e_s

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

     Return a matrix evaluating reproducing kernels for some L-splines
     at observed points.

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

     lspline(x,y=x, type="exp", ...)

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

       x: a numeric vector on which reproducing kerenls are evaluated. 

       y: an optional vector, specifying the second argument of
          reproducing kernels. Default is 'x'. 

    type: a string indicating the type of L-splines. Available options 
          are "exp", "logit","sine", "sine1", and "linSinCos". Default
          is "exp". 

     ...: other arguments needed.

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

     Denote L as the differential oprator, H_0 as the null (kernel)
     space. The available kernels correspond to the following L:

        *  exp: L=rD+D^2, H_0=span{1,exp(-rx)}. r>0, default to be 1;

        *  logit: L=D-1/(1+e^t), H_0=span{e^t/(1+e^t)};

        *  sine0: L=D^2+(2pi)^2, H_0=span{sin(2pi x),cos(2pi x)};

        *  sine1: L=D(D^2+(2pi)^2), H_0=span{1, sin(2pi x),cos(2pi x)};

        *  linSinCos: L=D^4+D^2, H_0=spac{1, x, sin(x), cos(x)}.

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

     a matrix with the numbers of row and column equal to the lengths
     of x and y respectively. The [i, j] element is the reproducing
     kernel evaluated at (x[i], y[j]).

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

     Chunlei Ke chunlei_ke@pstat.ucsb.edu and Yuedong Wang
     yuedong@pstat.ucsb.edu

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

     Wahba, G. (1990). Spline Models for Observational Data. SIAM, Vol.
     59.

     Heckman, N and Ramsay, J. O. (2000). Penalised regression with
     model-based penalties. To appear in Canadian Journal of
     Statisitcs.

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

     'ssr'

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

     x<- seq(0,1, len=20)
     lspline(x, type="exp", r=1.5)

