Thin                 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 _T_h_i_n _P_l_a_t_e _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 thin plate
     splines at observed points.

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

     tp.pseudo(s, u=s, order=2)
     tp(s, u=s, order=2)

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

       s: a list or matrix of observations. One component, if a list,
          and one column, if a matrix, contains observations on one
          variable. If a list, all components must be of the same
          length.  

       u: a list or matrix of observations. If a list, all components
          must be of the same length. The number of componets of the
          list, or the number of column of the matrix must be the same
          as that for s.  Default is s. 

   order: an optional integer specifying the order of the thin plate
          spline. Default is 2. Let d be the dimension of s (and u).
          Then order must satisfy 2*order-d>0. 

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

     The pseudo kernel, which is conditional definite positive instead
     of definite positive, is easy to calculate, while the true
     reproducing kernel is complicated. Pseudo Kernels are enough to
     compute  spline estimates, but to calcualte Bayesian confidnece
     intervals, the true kernel is required.

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

     a matrix with the numbers of row and column equal to the common
     length of componets or  the number of row of s and t respectively.
     The [i, j] element is the pseudo or true reproducing kernel
     evaluated at the ith element of s and jth element of u.

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

     Chunlei Ke chunlei_ke@yahoo.com 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.

     Gu, C. and Wahba, G (1993). Smoothing Spline ANOVA with
     component-wise Bayesian confidence intervals. Journal of
     Computational and Graphical Statistics 55, 353-368.

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

     'ssr', 'cubic'

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

     data(acid)
     ## Not run: tp.pseudo(list(acid$x1, acid$x2))
     ## Not run: tp.pseud0(list(acid$x1, acid$x2), order=3)

