To calculate a spline estimate with multiple smoothing parameters
dmudr(y, q, s, weight = NULL, vmu = "v", theta = NULL, varht = NULL,
tol = 0, init = 0, prec = 1e-06, maxit = 30)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 \(info=rank(S)+1\).
fitted values.
estimates of c.
estimates of d.
vector of residuals.
estimate of variance.
estimates of parameters \(log10(\theta)\).
the estimate of \(log10(nobs*\lambda)\).
the minimum GCV/GML/UBR score at the estimated smoothing parameters.
equavilent degree of freedom.
length(y), number of observations.
dim(\(H_0\)), number of bases.
length(rk), number of reproducing kernels.
changed from the inputs.
a numerical vector representing the response.
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.
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.
a weight matrix for penalized weighted least-square: \((y-f)'W(y-f)+n\lambda J(f)\). Default is NULL for iid random errors.
a character string specifying a method for choosing the smoothing parameter. "v", "m" and "u" represent GCV, GML and UBR respectively. "u\(\sim\)", only used for non-Gaussian family, specifies UBR with estimated variance. Default is "v".
If `init=1', theta includes intial values for smoothing parameters. Default is NULL.
needed only when vmu="u", which gives the fixed variance in calculation of the UBR function. Default is NULL.
the tolerance for truncation in the tridiagonalization. Default is 0.0.
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.
precision requested for the minimum score value, where precision is the weaker of the absolute and relative precisions. Default is \(1e-06\).
maximum number of iterations allowed. Default is 30.
Chunlei Ke chunlei_ke@yahoo.com and Yuedong Wang yuedong@pstat.ucsb.edu
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
dsidr, gdsidr, gdmudr, ssr