dsidr                 package:assist                 R Documentation

_I_n_t_e_r_f_a_c_e _o_f _d_s_i_d_r _s_u_b_r_o_u_t_i_n_e_s _i_n _R_K_P_A_C_K

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

     To calculate a spline estimate with a single smoothing parameter

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

     dsidr(y, q, s=NULL, weight=NULL, vmu="v", varht=NULL, 
     limnla=c(-10, 3), job=-1, tol=0)

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

       y: a numerical vector representing the response. 

       q: a square matrix of the same order as the length of y, with
          elements equal to the reproducing kernel evaluated at the
          design points. 

       s: the design matrix of the null space H_0 of size
          (length(y),dim(H_0)),  with elements equal to the bases of
          H_0 evaluated at design points. Default is NULL, representing
          an empty NULL space.

  weight: A weight matrix for penalized weighted least-square:
          (y-f)'W(y-f)+nlambda J(f). Default is NULL for iid random
          errors. 

     vmu: a character string specifying a method for choosing the
          smoothing  parameter.  "v", "m" and "u" represent GCV, GML
          and UBR respectively.  "u~", only used for non-Gaussian
          family, specifies UBR with estimated variance. Default is
          "v". 

   varht: needed only when vmu="u", which gives the fixed variance in
          calculation of the UBR function. Default is NULL. 

  limnla: a vector of length 2, specifying a search range for the  n
          times smoothing parameter on log10 scale. Default is (-10,
          3). 

     job: an integer representing the optimization method used to find
          the smoothing parameter.  The  options are job=-1:
          golden-section search on (limnla(1), limnla(2));  job=0:
          golden-section search with interval specified automatically; 
          job >0: regular grid search on  [limnla(1), limnla(2)] with
          #(grids) = job + 1. Default is -1.  

    tol : tolerance for truncation used in `dsidr'. Default is 0.0,
          which sets to square of machine precision. 

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

    info: an integer that provides error message. info=0 indicates
          normal termination, info=-1 indicates dimension error,
          info=-2 indicates F_{2}^{T} Q F_{2} !>= 0, info=-3 indicates
          vmu is out of scope, and info>0 indicates the matrix S is
          rank  deficient with info=rank(S)+1.  

     fit: fitted values. 

       c: estimates of c. 

       d: estimates of d. 

    resi: vector of residuals. 

   varht: estimate of variance. 

   nlaht: the estimate of log10(nobs*lambda). 

  limnla: searching range for nlaht.  

   score: the minimum GCV/GML/UBR score at the estimated smoothing
          parameter. When job>0, it gives a vector of GCV/GML/UBR
          functions evaluated at regular grid points. 

      df: equavilent degree of freedom. 

    nobs: length(y), number of observations. 

   nnull: dim(H_0), number of bases. 

s,qraux,jpvt: QR decomposition of S=FR, as from Linpack `dqrdc'. 

       q: first dim(H_0) columns gives F^{T} Q F_{1}, and its
          bottom-right corner gives tridiagonalization of F_{2}^{T} Q
          F_{2}. 

_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:

     Gu, C. (1989). RKPACK and its applications: Fitting smoothing
     spline models. Proceedings of the Statistical Computing Section,
     ASA, 42-51.

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

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

     'dmudr', 'gdsidr', 'gdmudr', 'ssr'

