To calculate a spline estimate with a single smoothing parameter
dsidr(y, q, s=NULL, weight=NULL, vmu="v", varht=NULL,
limnla=c(-10, 3), job=-1, tol=0)
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.
fitted values.
estimates of c.
estimates of d.
vector of residuals.
estimate of variance.
the estimate of log10(nobs*lambda).
searching range for nlaht.
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.
equavilent degree of freedom.
length(y), number of observations.
dim(\(H_0\)), number of bases.
QR decomposition of S=FR, as from Linpack `dqrdc'.
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 numerical vector representing the response.
a square matrix of the same order as the length of y, with elements equal to the reproducing kernel evaluated at the design points.
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.
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".
needed only when vmu="u", which gives the fixed variance in calculation of the UBR function. Default is NULL.
a vector of length 2, specifying a search range for the n times smoothing parameter on \(log10\) scale. Default is \((-10, 3)\).
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 the number of grids = job + 1. Default is -1.
tolerance for truncation used in `dsidr'. Default is 0.0, which sets to square of machine precision.
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.
dmudr, gdsidr, gdmudr, ssr