dsidr: Interface of dsidr subroutines in RKPACK
In assist: A Suite of R Functions Implementing Spline Smoothing Techniques

dsidr

R Documentation

Interface of dsidr subroutines in RKPACK

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)

`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)+n\lambda 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`\sim`", 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 the number of grids = job + 1. Default is -1.
`tol`	tolerance for truncation used in ‘dsidr’. Default is 0.0, which sets to square of machine precision.

`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}`.

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.