assist (version 2.0)

dsidr: Interface of dsidr subroutines in RKPACK

Description

To calculate a spline estimate with a single smoothing parameter

Usage

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

Arguments

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 sea

tol

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

Value

• 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 $F_{2}^{T} Q F_{2}$.

References

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.

See Also

dmudr, gdsidr, gdmudr, ssr