dmudr                 package:assist                 R Documentation

_I_n_t_e_r_f_a_c_e _o_f _d_m_u_d_r _s_u_b_r_o_u_t_i_n_e _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 multiple smoothing parameters

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

     dmudr(y, q, s, weight = NULL, vmu = "v", theta = NULL, varht = NULL, 
         tol = 0, init = 0, prec = 1e-06, maxit = 30)

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

       y: a numerical vector representing the response. 

       q: a list, or an array, of square matrices of the same order as
          the length of y, which are the reproducing kernels evaluated
          at the design points. 

       s: the design matrix of the null space H_0 of size
          (length-of-y,dim(H_0)), with elements equal to the bases of
          H_0 evaluated at design points. 

  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". 

   theta: If `init=1', theta includes intial values for smoothing
          parameters. Default is NULL. 

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

     tol: the tolerance for truncation in the tridiagonalization.
          Default is 0.0. 

    init: an integer of 0 or 1 indicating if initial values are
          provided for theta. If init=1, initial values are provided
          using theta. Default is 0. 

    prec: precision requested for the minimum score value, where
          precision is the weaker of the absolute and relative
          precisions. Default is 1e-06. 

   maxit: maximum number of iterations allowed. Default is 30. 

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

    info: an integer that provides error message. info=-1 indicates
          dimension error,  info=-2 indicates F_{2}^{T} Q_{*}^{theta}
          F_{2} !>= 0, info=-3 indicates tuning parameters are out of
          scope, info=-4 indicates fails to converge within maxite
          steps, info=-5 indicates fails to find a reasonable descent
          direction, 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. 

   theta: estimates of parameters log10(theta). 

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

   score: the minimum GCV/GML/UBR score at the estimated smoothing
          parameters.  

      df: equavilent degree of freedom. 

    nobs: length(y), number of observations. 

   nnull: dim(H_0), number of bases. 

      nq: length(rk), number of reproducing kernels. 

   s,q,y: changed from the inputs. 

_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:

     'dsidr', 'gdsidr', 'gdmudr', 'ssr'

